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Which expression is equivalent to StartRoot StartFraction 55 x Superscript 7 Baseline y Superscript 6 Baseline Over 11 x Superscript 11 Baseline y Superscript 8 Baseline EndFraction EndRoot? Assume x > 0 and y Greater-than 0. StartFraction x squared StartRoot 5 EndRoot Over y EndFraction StartFraction y StartRoot 5 EndRoot Over x squared EndFraction StartFraction StartRoot 5 EndRoot Over x squared y EndFraction StartFraction x StartRoot 5 EndRoot Over y EndFraction

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abidemiokin

The expression that is equivalent to the equation above is [tex]\frac{5}{x^4y^2}[/tex]

Given the expression:

[tex]\frac{55x^7y^6}{11x^{11}y^8}[/tex]

To solve this expression, we will use the law of indices as shown:

[tex]a^m \times a^n = a^{m+n}\\\frac{a^m}{a^n}=a^{m-n}\\[/tex]

Applying these laws to the equation above;

[tex]=\frac{55x^7y^6}{11x^{11}y^8}\\=\frac{55}{11} x^{7-11}y^{6-8}\\=\frac{55}{11} x^{-4}y^{-2}\\=5x^{-4}y^{-2}\\[/tex]

Also [tex]a^{-m}=\frac{1}{a^m}[/tex], therefore;

[tex]5x^{-4}y^{-2} = \frac{5}{x^4y^2}[/tex]

Therefore the expression that is equivalent to the equation above is [tex]\frac{5}{x^4y^2}[/tex]

Learn more on indices here: https://brainly.com/question/15361818

The simplified form of the given expression is  [tex]\dfrac{5}{x^{4}y^2}[/tex] and this can be determined by using the arithmetic operations.

Given :

Expression  --  [tex]\dfrac{55x^7y^6}{11x^{11}y^8}[/tex]

The following steps can be used in order to evaluate the given expression:

Step 1 - The arithmetic operations can be used in order to evaluate the given expression.

Step 2 - Write the given expression.

[tex]= \dfrac{55x^7y^6}{11x^{11}y^8}[/tex]

Step 3 - Simplify the above expression.

[tex]= \dfrac{55}{11x^{4}y^2}[/tex]

Step 4 - Divide 55 by 11 in the above expression.

[tex]= \dfrac{5}{x^{4}y^2}[/tex]

For more information, refer to the link given below:

https://brainly.com/question/25834626

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