Question

Which expression is equivalent to square root 55x^7y^6/11x^11y^8 ? Assume x > 0 and y > 0.

(ignore) Which expression is equivalent to ? Assume x > 0 and y  0.

Answer 1

The first step for solving this expression is to reduce the fraction with 11.
$\sqrt{ \frac{5 x^{7} y^{6} }{ x^{11} y^{8} } }$
Now reduce the fraction with $x^{7}$
$\sqrt{ \frac{5 y^{6} }{ x^{4} y^{8} } }$
Reduce the fraction with $y^{6}$
$\sqrt{ \frac{5}{ x^{4} y^{2} } }$
Lastly,, we need to remember our radical rules. They state that in order for us to take a root of a fraction,, we must take the root of the numerator and denominator separately. Knowing this rule,, this changes the expression to the following:
$\frac{ \sqrt{5} }{ x^{2} y}$
Since we cannot simplify the expression any further,, the correct answer to your question is going to be $\frac{ \sqrt{5} }{ x^{2} y}$,, or option C.
Let me know if you have any further questions.
:)

Answer 2

The equivalent expression of √55x⁷y⁶ / 11x¹¹y⁸ is $\frac{\sqrt{5} }{x^{2} y}$

√55x⁷y⁶ / 11x¹¹y⁸

Lets reduce the fraction by dividing the numerator and denominator by 11.

Therefore,

√5x⁷y⁶ / x¹¹y⁸

Using indices principle

x⁷ / x¹¹ = x⁷⁻¹¹ = x⁻⁴ = 1 / x⁴

y⁶ / y⁸ = y⁶⁻⁸ = y⁻² = 1 / y²

Therefore,

√5/ x⁴y²

square root of 1 / y² is 1 / y

square root of 1 / x⁴ is 1 / x²

Finally,

$\frac{\sqrt{5} }{x^{2} y}$

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