The formula for calculating the sample proportion is the number of occurrences ( x) divided by the sample size ( n ): p ^ = x n. In our example, 6 out of 30 were born in the US: x is 6, and n is 30. You can use any calculator for free without any limits. Free algebra and math word problems. Please enter the observed data, the hypothesized population proportions (expected proportions) and the significance level and the results of the Chi-Square test will be presented for you below: Observed ValuesExpected ProportionsCategories (OPTIONAL) Significance Level (\(\alpha\)) = Chi-Square Test for Goodness of . Absolute degree of an algebraic expression Calculator. Ratio and Proportion Practice Questions: Properties of Proportion. Multiply and split each regard to a percentage by the same number (non-zero), which does t impact the ratio. For instance, if the speed of a car is increased, it covers more distanceduring afixed amountof your time. This formula can be used to find the percent of a given ratio and to find the missing value of a part of a whole. n: Similarly, 2 * (x + 5) can also be entered as 2(x + 5); 2x * (5) can be entered as 2x(5). If the two resulting values are equal then the ratio is TRUE, otherwise is FALSE. The ratio of two quantities of the same kind and in the same units is a fraction that shows how many times one quantity is of the other. An equality of two ratios is called a proportion. Proportions of Cement Mortar a. Masonry Construction: Ordinary masonry work with brick/ stone as a structural unit. If \(a,b,c\) are in continued proportion, then \(b\) is the mean proportional between \(a\) and \(c.\). 3. (2 + 3)/3 = (x + y)/y If 6:2=8:x, then 6x=16 If AX:XB as AB:AC, find the missing length.AX = 5, XB = 4, AC = 6, find AB. 2D shape calculators 3D shape calculators Prime numbers Number . Using the natural log calculator, we get. The cross product property of proportions. Direct proportion2. A ratio (a:b) is simplest if its antecedent (a) and consequent (b) have no common factor other than (1.) Make sure one input should be unknown (x). In simple words, if one quantity increases, the other quantity decreases and vice-versa. Here, we have two ratios and one of them has an unknown value x. Plot the Graph and Identify the Proportion Plot the x and y coordinates on the graphs provided. Use this constant of proportionality Calculator to calculate the constant of proportionality that is based on two related values (x and y). Thus, the ratio of two numbers (a) and (b\left( {b \ne 0} \right)) is (a \div b) or, (\frac{a}{b}) and is denoted by (a:b. Each tool is carefully developed and rigorously tested, and our content is well-sourced, but despite our best effort it is possible they contain errors. Multiply the two extreme values and two mean values with each other respectively. The proportion calculator helps compute identical proportions. 5 goes into 40 eight times. The ratio is employed to match the dimensions of two things with an equivalent unit. On the app toolstrip, click Load Image, and then select Load Image from Workspace to load the image from the workspace into the app. Press the "Calculate h" button to open the calculation window. Three numbers \(a,\,b,\,c\) are in continued proportion if \(a,\,b,\,b,\,c\) are in proportion. \(c\) is called the third proportional to \(a\) and \(b\). On a mapof a sufficiently small geographical area, drawn to scaledistances, the distance between any two points on the map is directly proportional to the beeline distance between the two locations represented by those points; the constant of proportionality is the scale of the map. \(a\) and \(b\) could be any two quantities. In biology, flowering plants are known by the name angiosperms. The symbols to represent the proportion are :: or =. Properties of Proportions 1. The formula to calculate this confidence interval is: To find a confidence interval for a population proportion, simply fill in the boxes below and then click the Calculate button. Similarly, four quantities in continued proportion will have the ratio between the first and second equal to the ratio between the third and fourth. Assume that we have any two quantities (or two entities) and we have to find the ratio of these two, then the formula for ratio is defined as \(a:b \Rightarrow \frac{a}{b}\), where, For example, in ratio \(5:9\), is represented by \(\frac{5}{9}\), where \(5\) is antecedent and \(9\) is consequent. Looking for someone to help you with algebra? The ratio of a a to b b can also be expressed as a:b a: b or \dfrac {a} {b} ba. Previous Properties of Proportions Next Similar Triangles 1. 4. The proportion between a,b and u,v would appear as follows if the fraction layout is used. When you have two ratios with values expected to be equal, certain steps of simplification are performed. The power of a product is equal to the product of it's factors raised to the same power, Simplify $\left(x^2\right)^5$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. The first of these steps is cross multiplication. Use the following as a guide: Any lowercase letter may be used as a variable. Exponents may not be placed Q.4: What is proportion?Ans: An equality of two ratios is called a proportion. From the above example, we can say that product of extreme terms \( = 40 \times 350 = 14000\) and product of mean terms \( = 70 \times 200 = 14000\), Therefore, a product of extreme terms \(=\) product of mean terms. Fantastic Calculator! Calculator.tech provides online calculators for multiple niches including mathematical, financial, Health, informative, Chemistry, physics, statistics, and conversions. attempts to use the / symbol will result in an error. Continue reading the article to know more details like the types of properties of proportions, the difference between the ratio and proportion properties and more. The Formula for Percent Proportion is Parts /whole = percent/100. Inequalities Calculator. A ratio is a comparison of two quantities. Learn more about us. Keywords: definition; means extremes; image/svg+xml.
, If \(p:q = q:r,\) then \(p,\,q,\,r\) are said to be in continued proportion. Q.3: The first three terms of a proportion are 3,5 and 21, respectively. A Proportion Calculator is a free online tool that displays a proportion of a given expression. Step 2: Enter the values in the given input boxes and select the variable whose value needs to be determined (x or y). In other words, in a proportion, a/b = c/d. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); Statology is a site that makes learning statistics easy by explaining topics in simple and straightforward ways. proportionality, In algebra, equality between two ratios. Introduction to Statistics is our premier online video course that teaches you all of the topics covered in introductory statistics. Once you click away on our proportional relationship calculator and determine two variables that are directly or indirectly proportional to each other in a fraction of seconds. [Example] What skills are tested? May 3, 2016. Use the reciprocal property. Example: 1/2 = x/x will cause the calculator to report For example, if the speed of a car is increased, it covers more distance in a fixed amount of time. A proportion is an equation or equality of the two ratios, and we can write proportions to estimate equivalent ratios and work for unknown quantities. Now, we need to perform cross multiplication to proceed with the process of calculating proportion. Ratio Form Is light a wave or a particle? Addition of numbers Calculator. In Mathematics, a proportion is defined as a statement that the two ratios should be equal. Your Mobile number and Email id will not be published. 4. We have provided some frequently asked questions about Properties of Proportion here: Q.1: What is the difference between ratio and proportion?Ans: Ratio: The ratio is employed to match the dimensions of two things with an equivalent unit. Therefore, the ratio of rotten mangoes to the mangoes bought is \(3:12.\)Therefore, \(x:100 = 3:12\)\( \Rightarrow x \times 12 = 100 \times 3\)\( \Rightarrow 12x = 300\)\( \Rightarrow x = 25\)Thus, there will be \(25\) rotten mangoes if I buy \(100\) mangoes. The proportion calculator solves for \(x\). A proportion is two ratios that have been set equal to each other, for example, 1/4 equals 2/8. This type describes the direct relationship between two quantities. Similarly, if we have two unknown values in a relation, we can use cross . Based on the type of relationship two or more quantities share, the proportion can be classified into different types. { "@context": "https://schema.org", "@type": "FAQPage", "mainEntity": [{ "@type": "Question", "name": "What Is A Proportion? Leading AI Powered Learning Solution Provider, Fixing Students Behaviour With Data Analytics, Leveraging Intelligence To Deliver Results, Exciting AI Platform, Personalizing Education, Disruptor Award For Maximum Business Impact, Copyright 2023, Embibe. In this article, we studied the definition of ratio and proportion properties, addition property of proportion, properties of proportion calculator, properties of proportions worksheet, and more. Componendo and dividendo If \(a : b = c : d\), then \(a + b : a b = c + d : c d\). This is shown as a proportion below. In the expression, $m$ equals $2$ and $n$ equals $4\cdot 2$, Simplify $\left(x^3\right)^3$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. Need some help? Through proportion concepts, the value of X has to be determined. For instance, consider that we have the following two ratios which are considered to be equal. The proportion math definition is when two ratios or fractions are equal to each other. Invertendo If \(a : b = c : d\), then \(b : a = d : c\) Multiplication and Division, Addition and Subtraction. The calculator uses cross multiplication to convert proportions into equations which Open the Image Region Analyzer app from the MATLAB toolstrip. In notation, an inverse proportion is written as y 1/x. Example: Given the equation \(\mathbf{\frac{4}{10} = \frac{x}{15}}\) solve for \(x\). Some of the examples of proportion are: Enter the ratios in the respective input field, Now click the button Solve to get the result, Finally, the true or false for the given proportion will be displayed in the output field. When two or more such ratios are equivalent, they are said to be in proportion. In the expression, $m$ equals $2$ and $n$ equals $5$, Simplify $\left(y^3\right)^5$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. Properties of Proportion A proportion is a situation in which 2 ratios are equal. Addition of integers Calculator. To solve proportion problems, we use the concept that proportion is two ratios that are equal to each other. Indirect or inverse proportion, Q.3: What is continued and mean proportion?Ans: Three numbers \(a,\,b,\,c\) are in continued proportion if \(a,b,b,c\) are in proportion. Q.5: For every 12 mangoes that I buy, 3 turn out to be rotten. The calculator follows the standard order of operations taught by most algebra books Parentheses, Exponents, The Proportion Calculator is used to solve proportion problems and find the missing value in a proportion (Step by Step). The ratio is a way of corresponding two portions of the identical kind by utilising division. If either side of the proportion has a numerator and denominator that share a common factor with a variable, \dfrac {a} {b} = \dfrac {u} {v} ba = vu In the fraction form, a forward slash sign "/" is used between each pair of numbers. Suppose that if the value of (ab)\Big(\dfrac{a}{b}\Big)(ba)is 10 then (uv)\Big(\dfrac{u}{v}\Big)(vu)would have a value of 10 as well. Find online algebra tutors or online math tutors in a couple of clicks. You want to plan research that will reject the null assumption if the population proportion is 0.75 or larger. Suppose the value of 'x' is unknown. An equation that represents that the two given ratios are equivalent to each other is called a proportion. How do you know if a relationship is proportional? Q.2: Are 4,12,36 in continued proportion?Ans: We know that three numbers \(a,b,c\) are in continued proportion if \(a,b,b,c\) are in proportion.Therefore, \(4,12,36\) will be in continued proportion if \(4,12,12,36\) are in proportion.We have the product of extreme terms \( = 4 \times 36 = 144\)Product of mean \( = 12 \times 12 = 144\)Therefore, the product of extreme terms \(=\) product of means\( \Rightarrow 4,12,12,36\) are in proportion.\( \Rightarrow 4,12,36\) are in continued proportion. So, if its first and second term is multiplied or divided by the same non-zero number, a ratio does not alter. Male and female reproductive organs can be found in the same plant in flowering plants. The proportion of the population voting for Mr. Jones is. Complete this proportion: 3 : 5 = x : 40. Cross multiplying works because youre just multiplying both sides of the equation by 1. [Examples] A proportion is an equality of two ratios. We all know that a proportion is an expression which states that the two ratios are equal. Before we can use the calculator, it's important to understand what a proportion is and how to solve proportions by hand. Here, \(a\) and \(b\) are any two integers. Three quantities a, b, c of the same kind (in same units) are said to be in continuous proportion. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and . The estimate of the proportion is first modified to give the Wilson point estimator (p W) thus: z is the (1 /2) percentile of the standard normal distribution where is the significance level; for a 95% confidence interval z = 1.96 2. n is the sample size. Solving a proportion means that you are missing one part of one of the fractions, and you need to find that missing value. This proportion calculator can solve ratios in case a value is missing or even two values are missing from the given proportion or can evaluate as true or false any proportions. Finally figured my equip load in Dark Souls, thank you!! Fill in the sample size, n, the number of successes, x, the hypothesized population proportion p 0, and indicate if the test is left tailed, <, right tailed, >, or two tailed, . Since the denominators are also the same here, b d, you can remove them and say that: This is the result of cross multiplying the original equation: Proportion is explained majorly based on ratios and fractions. Step 1: Go to Cuemath's online proportions calculator. Example 1: The time taken by a car is covering a certain distance is inversely proportional to the speed of the car. The ratio is a way of comparing two quantities of the same kind by using division. n is the sample size. Step 2: Create a mathematical equation that describes the situation. What is a proportion in a math calculator? Get started with our course today. Also, \(40,\,70,\,200\) and \(350\) are in proportion because \(40:70 = 200:350\). For instance, consider the following.. . Our first ratio of the number of girls to boys is \(2:5\) and that of the other is \(4:8\), then the proportion can be written as \(2:5::4:8\) or \(\mathbf{\frac{2}{5} = \frac{4}{8}\). Regular polygon calculator is an online tool to calculate the various properties of a polygon. Watch this tutorial to learn more! In the expression, $m$ equals $4$ and $n$ equals $2$, Simplify $\left(\left(y^2\right)^4\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. If you multiply both sides by \(1\) using the denominators from the other side of the equation you get: $$\mathbf{\frac{a}{b}\times \frac{d}{d}= \frac{c}{d}\times \frac{b}{b}}$$. Pandas: How to Use Variable in query() Function, Pandas: How to Create Bar Plot from Crosstab. on numbers, brackets, or parentheses. Advanced differentiation Calculator. To do that, you'll need to factor in the properties of the normal distribution. Solved Example: Find the fourth proportional of 3, 4 and 18. To find . Switching the means or the extremes in a proportion will result in a proportion. The mean proportion between \(a\) and \(b\) is \(\sqrt(ab)\). The fraction form The proportion between a,b and u,v would appear as follows if the fraction layout is used. 4 x 4 = 100 4. 366=X10\dfrac{36}{6} = \dfrac{X}{10}636=10X. Free online converters. This engineering data is often used in the design of structural beams . However, the values making an upward slope are (6 and X). When two ratios are of equal value, then the values are in equal proportion. Then hit "Calculate" and the test statistic and p-Value will be calculated for you. 2) The quantities a, b, c, and d are the "terms" of the proportion. Thus, multiplying the first ratio by c and the second ratio by b, we have. On the Apps tab, in the Image Processing and Computer Vision section, click Image Region Analyzer . Hence, the following statement would be constructed after equating them. What are ratios and proportions? Therefore, 3 : 4 = 18 : x 3 x = 4 18; from the above property (vi) we know product of extremes = product of means 3x = 72 x = 72/3 In the expression, $m$ equals $9$ and $n$ equals $2$, Simplify $\left(y^{12}\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. When two or more such ratios are equal, they are said to be in proportion. Consider two ratios, \(3:24\) and \(4:36.\) We find that \(3:24 = 1:8\) and \(4:32 = 1:8.\) So, \(3:24 = 4:32\) is a proportion. Proportion is expressed using the double colon \(\left( {::} \right)\) or adequate to the symbol \(\left( = \right).\) Proportion is an equation. Introduction to Statistics is our premier online video course that teaches you all of the topics covered in introductory statistics. At Wyzant, connect with algebra tutors and math tutors nearby. (More speed, Less is the time taken to cover a distance .) Fourth, 3rd and also Mean Symmetrical. The proportion c,dc,dc,d and e,fe,fe,f would appear in the following way if the ratio layout is used. From the above-given example, = 4/16 are in proportion, because, when the right-hand side is simplified, we get the ratio of the left-hand side. Confidence Interval for Proportion Calculator A confidence interval for a population proportion is a range of values that is likely to contain a population proportion with a certain level of confidence. Multiply and divide each term of a ratio by the same number (non-zero), which doesnt affect the ratio. Measures of Central Tendency: Definition & Examples. Reciprocal Property : If two ratios are equal, then their reciprocals are also equal. Also, we have studied the properties of proportion, and different types of proportion and solved some example problems on the same. Ratios and Proportions: Definition Definition of Ratio: A ratio is a comparison of two or more numbers that indicates their quantities in relation to each other. Required fields are marked *. Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. This math tool allows you solve ratios in any of the following situations: The formulas used by this proportion calculator are: 2. 8 pens cost 2.16. Find its fourth term.Ans: Let the fourth term be \(x.\)Then, \(3,5,21,\,x\) are in proportion.\( \Rightarrow 3 \times x = 5 \times 21\)\( \Rightarrow 3x = 5 \times 21\)\( \Rightarrow x = \frac{{5 \times 21}}{3}\)\( \Rightarrow x = 5 \times 7 = 35.\), Q.4: What must be added to the numbers 6,10,14 and 22 to be in proportion?Ans: Let the required number be \(x.\)Then, \(6 + x,\,10 + x,\,14 + x,\,22 + x\) are in proportion.\( \Rightarrow \) Product of extreme terms \(=\) product of mean terms.\( \Rightarrow \left( {6 + x} \right)\left( {22 + x} \right) = \left( {10 + x} \right)\left( {14 + x} \right)\)\( \Rightarrow 132 + 6x + 22x + {x^2} = 140 + 10x + 14x + {x^2}\)\( \Rightarrow 132 + 28x = 140 + 24x\)\( \Rightarrow 28x 24x = 140 132\)\( \Rightarrow 4x = 8\)\( \Rightarrow x = 2\)Hence, the required number is \(2.\), NCERT Solutions for Chapter-Ratio and Proportion. 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Required fields are marked *. Since three quantities a, b, c are in continuous proportion, we can write them as Solve the proportion between 2 fractions and calculate the missing fraction variable inequalities. Q.2: What are the types of proportion?Ans: There are two basic types of proportion, namely1. You should know that the fraction one-half is equal to two-fourths. All rights reserved, Properties of Proportion: Types, Differences, Examples, All About Properties of Proportion: Types, Differences, Examples, JEE Advanced Previous Year Question Papers, SSC CGL Tier-I Previous Year Question Papers, SSC GD Constable Previous Year Question Papers, ESIC Stenographer Previous Year Question Papers, RRB NTPC CBT 2 Previous Year Question Papers, UP Police Constable Previous Year Question Papers, SSC CGL Tier 2 Previous Year Question Papers, CISF Head Constable Previous Year Question Papers, UGC NET Paper 1 Previous Year Question Papers, RRB NTPC CBT 1 Previous Year Question Papers, Rajasthan Police Constable Previous Year Question Papers, Rajasthan Patwari Previous Year Question Papers, SBI Apprentice Previous Year Question Papers, RBI Assistant Previous Year Question Papers, CTET Paper 1 Previous Year Question Papers, COMEDK UGET Previous Year Question Papers, MPTET Middle School Previous Year Question Papers, MPTET Primary School Previous Year Question Papers, BCA ENTRANCE Previous Year Question Papers, The numbers \(a,\,b,\,c\) and \(d\) are proportional if the ratio of the first two quantities is equal to the ratio of the last two quantities, i.e., \(a:b::c:d\) and is read as \(a\) is to \(b\) is as \(c\) is to \(d.\) The symbol \(::\) stands for is as.
, Each quantity in a proportion is called its term, or it is proportional. The flower is the sexual reproduction organ. How to Solve Proportion Problems with This Calculator? In other words, we can write the following statement to elaborate on this point. In simple words, if one quantity increases, the opposite quantity decreases and vice-versa. You could use any of the four numbers from the given set of five numbers and set up two equal ratios to form a proportion. Enter below the shape dimensions. We write proportions to help us establish equivalent ratios and solve for unknown quantities. The output indicates that a total of 450 . (3 out of 5 is how many out of 40?) 1 : to adjust (a part or thing) in size relative to other parts or things 2 : to make the parts of harmonious or symmetrical 3 : apportion, allot Phrases in proportion : proportional sense 1 Synonyms Noun balance coherence concinnity consonance consonancy harmony orchestration symmetry symphony unity See all Synonyms & Antonyms in Thesaurus symbol. If \(ad \ne bc,\) then \(a,\,b,\,c,\,d\) are not in proportion. Common examples of direct proportionality include: Examples of proportionality varying inversely include: Our proportions calculator can be used to construct and check many more examples. Enter P 1 = 0.7 and P 2 = 0.75. Simple Interest Compound Interest . 0 as a solution, even though there is no solution. Free Algebraic Properties Calculator - Simplify radicals, exponents, logarithms, absolute values and complex numbers step-by-step . you can contact us anytime. The calculator uses cross multiplication to convert proportions into equations which are then solved using ordinary equation solving methods. Middle School Math Solutions - Expand Calculator, Perfect Squares . It is expressed using the double colon (::) or equal to the symbol (=). Consider the numbers\(40,\,70,\,200\,350.\) We find that \(40:70 = 200:350.\) So, the given numbers are in proportion. A ratio is a comparison of two quantities. This in general, would be the LCM of means, and for the given ratio, the LCM of b & c will be bc. Your Mobile number and Email id will not be published. (a) m E = 90 ( E and A are corresponding angles of similar polygons, and corresponding angles of similar polygons are equal.) We hope you find this article onProperties of Proportion helpful. Area Moment of Inertia Section Properties: Parabolic Spandrel Section Properties Calculator. Proportion finds application in solving many daily life problems such as in business while dealing with transactions or while cooking, etc. Proportion is an equation. $\frac{\left(\left(3x y^2\right)^4\left(2x^3 y^4\right)^3\right)^2}{\left(4x^2 y^3\right)^5}$, $\frac{\left(\left(3xy^2\right)^4\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2y^3\right)^5}$, $\frac{\left(\left(3xy^2\right)^4\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(\left(3xy^2\right)^4\right)^2\left(\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\left(xy^2\right)^4\right)^2\left(\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\right)^2\left(\left(xy^2\right)^4\right)^2\left(\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\right)^2\left(x^4\left(y^2\right)^4\right)^2\left(\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\right)^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\right)^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\left(x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\right)^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\right)^2\left(\left(x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\right)^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\right)^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{81^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{6561\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{6561\left(x^4\right)^2\left(\left(y^2\right)^4\right)^28^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{6561\cdot 64\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{419904\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{419904\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}\left(y^3\right)^5}$, $\frac{419904\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$, $\frac{419904x^{4\cdot 2}\left(\left(y^2\right)^4\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$, $\frac{419904x^{4\cdot 2}\left(y^2\right)^{4\cdot 2}\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$, $\frac{419904x^{4\cdot 2}y^{2\cdot 4\cdot 2}\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$, $\frac{419904x^{4\cdot 2}y^{2\cdot 4\cdot 2}\left(x^{3\cdot 3}\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$, $\frac{419904x^{4\cdot 2}y^{2\cdot 4\cdot 2}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$, $\frac{419904x^{4\cdot 2}y^{2\cdot 4\cdot 2}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{10}y^{3\cdot 5}}$, $\frac{419904x^{4\cdot 2}y^{2\cdot 4\cdot 2}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{10}y^{15}}$, $\frac{419904x^{8}y^{2\cdot 4\cdot 2}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{10}y^{15}}$, $\frac{419904x^{8}y^{8\cdot 2}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{10}y^{15}}$, $\frac{419904x^{8}y^{16}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{10}y^{15}}$, $\frac{419904x^{8}y^{16}\left(x^{9}y^{4\cdot 3}\right)^2}{1024x^{10}y^{15}}$, $\frac{419904x^{8}y^{16}\left(x^{9}y^{12}\right)^2}{1024x^{10}y^{15}}$, $\frac{419904x^{8}y^{\left(16-15\right)}\left(x^{9}y^{12}\right)^2}{1024x^{10}}$, $\frac{419904x^{8}y^{1}\left(x^{9}y^{12}\right)^2}{1024x^{10}}$, $\frac{419904x^{8}y\left(x^{9}y^{12}\right)^2}{1024x^{10}}$, $\frac{419904y\left(x^{9}y^{12}\right)^2}{1024x^{\left(10-8\right)}}$, $\frac{419904y\left(x^{9}y^{12}\right)^2}{1024x^{2}}$, $\frac{419904y\left(x^{9}\right)^2\left(y^{12}\right)^2}{1024x^{2}}$, $\frac{419904yx^{9\cdot 2}\left(y^{12}\right)^2}{1024x^{2}}$, $\frac{419904yx^{9\cdot 2}y^{12\cdot 2}}{1024x^{2}}$, $\frac{419904yx^{18}y^{12\cdot 2}}{1024x^{2}}$, $\frac{419904y^{\left(24+1\right)}x^{18}}{1024x^{2}}$, $\frac{419904y^{25}x^{\left(18-2\right)}}{1024}$, $\frac{\sqrt{2x^{12} y^{21} z^8}}{40\sqrt{xy\cdot z}}$, $\left(x\left(x^{2\left(x\left(x^2\right)^{\frac{1}{3}}\right)^{\frac{1}{3}}}\right)^{\frac{1}{3}}\right)^{\frac{1}{3}}$, $\left(7x^{\frac{2}{3}}\left(x y^{121\left(-1\right)}\right)^{\frac{1}{2}}\right)^4$, $\left(1\left(81\right)\left(-1\right)\right)^{\frac{1}{4}}$, $\frac{\left(x^{\frac{1}{5}} y^{\frac{3}{2}}\right)^{10}}{\left(y^{\left(-1\right)\cdot\frac{2}{5}} x^{\frac{2}{3}}\right)^5}$, $\frac{\left(4x^{121\left(-1\right)} y^4 z^8\right)^3}{\left(9x y^3 z^5\right)^4}$, $\frac{\left(-5x^3 y^2\right)^3\left(x y^5\right)^2}{\left(-5x^{-1}\cdot y\right)^{-1}}$.