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Which expression is equivalent to RootIndex 4 StartRoot StartFraction 16 x Superscript 11 Baseline y Superscript 8 Baseline Over 81 x Superscript 7 Baseline y Superscript 6 Baseline EndFraction EndRoot? Assume x Greater-than 0 and y not-equals 0. StartFraction 4 x (RootIndex 4 StartRoot y squared EndRoot) Over 9 EndFraction StartFraction 2 x (RootIndex 4 StartRoot y squared EndRoot) Over 3 EndFraction StartFraction 4 x squared y Over 9 EndFraction StartFraction 2 x squared y Over 3 EndFraction

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Answer:

I said D

Step-by-step explanation:

MrRoyal

The equivalent expression of the expression[tex]\sqrt[4]{\frac{16x^{11}y^8}{81x^7y^6}}[/tex] is  [tex]\frac 23x\sqrt{y[/tex]

How to determine the equivalent expression?

The expression is given as:

[tex]\sqrt[4]{\frac{16x^{11}y^8}{81x^7y^6}}[/tex]

Take the 4th root of 16 and 81

[tex]\frac 23\sqrt[4]{\frac{x^{11}y^8}{x^7y^6}}[/tex]

Apply the law of indices

[tex]\frac 23\sqrt[4]{x^{11 - 7}y^{8 - 6}}[/tex]

Evaluate the difference

[tex]\frac 23\sqrt[4]{x^{4}y^{2}}[/tex]

Take the 4th root of x^4

[tex]\frac 23x\sqrt[4]{y^{2}}[/tex]

Take the 4th root of y^2

[tex]\frac 23x\sqrt{y[/tex]

Hence, the equivalent expression of [tex]\sqrt[4]{\frac{16x^{11}y^8}{81x^7y^6}}[/tex] is  [tex]\frac 23x\sqrt{y[/tex]

Read more about equivalent expression at:

https://brainly.com/question/2972832

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