Question

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

algebra II engenuity

Answer 1

Answer: Last option.

Explanation:

You need to apply the Quotient of powers property:

`(a^m)/(a^n) =a^((m-n))`

Then:

`\sqrt{(128x^5y^6)/(2x^7y^5)} =\sqrt{(64y)/(x^2)}`

Remember that:

`64=8*8=8^2`

Then you can rewrite the expression:

`=\sqrt{(8^2y)/(x^2)}`

Finally, since
`\sqrt[n]{a^n}=a`, you get:

`=(8√(y) )/(x)`

Answer 2

Last option

Explanation:

Given expression is:

`\sqrt{(128x^5y^6)/(2x^7y^5) }`

The terms can be simplified one by one

`=\sqrt{(64x^5y^6)/(x^7y^5) }`

As the larger power of x is in numerator, the smaller power will be brought to denominator

`=\sqrt{(64y^6)/(x^((7-5))y^5)}\\=\sqrt{(64y^6)/(x^(2)y^5)}`

Similarly for y,

`=\sqrt{(64y^((6-5)))/(x^(2))}\\=\sqrt{(64y)/(x^(2))}`

Applying the radical

`\sqrt{(8^2*y)/(x^(2))}\\So\ the\ answer\ will\ be\\= (8√(y))/(x)`

So, last option is the correct answer ..