Question

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

Answer 1

Answer:

The correct answer is third option

√5/(x²y)

Step-by-step explanation:

It is given an expression,√(55x⁷y⁶/11x¹¹y⁸)

Points to remember

Identities

xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ)

x⁻ⁿ = x¹/ⁿ

To find the equivalent expression

We have, √(55x⁷y⁶/11x¹¹y⁸)

By using above identity we can write,

√(55x⁷y⁶/11x¹¹y⁸) = √[(55/11) (x⁷/x¹¹) (y⁶/y⁸)]

 = √[5x⁷⁻¹¹ y⁶⁻⁸]

 = √[5x⁻⁴ y⁻²]

 = √[5/x⁴y²]

 = √5/(x²y)

Therefore the correct answer is third option

√5/(x²y)

Answer 2

Answer:

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

Step-by-step explanation: