Question

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

Answer 1

Basically the answer is C.

Answer 2

The first step for solving this expression is to reduce the fraction with 11.

`\sqrt{ (5 x^(7) y^(6) )/( x^(11) y^(8) ) }`
Now reduce the fraction with
`x^(7)`.

`\sqrt{ (5 y^(6) )/( x^(4) y^(8) ) }`
Reduce the fraction one more time with
`y^(6)`.

`\sqrt{ (5)/( x^(4) y^(2) ) }`
To take the root of a fraction,, we must take the root of the numerator and denominator separately. This rule will change the expression to the following:

`( √(5) )/( x^(2) y)`
Since we cannot simplify this fraction any further,, the final answer is going to be
`( √(5) )/( x^(2) y)`.
Let me know if you have any further questions.
:)