Question

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

Answer 1

Answer: Last option.

Step-by-step explanation:

You need to apply the Quotient of powers property:

$\frac{a^m}{a^n} =a^{(m-n)}$

Then:

$\sqrt{\frac{128x^5y^6}{2x^7y^5}} =\sqrt{\frac{64y}{x^2}}$

Remember that:

$64=8*8=8^2$

Then you can rewrite the expression:

$=\sqrt{\frac{8^2y}{x^2}}$

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

$=\frac{8\sqrt{y} }{x}$

Answer 2

Answer:

Last option

Step-by-step explanation:

Given expression is:

$\sqrt{\frac{128x^5y^6}{2x^7y^5} }$

The terms can be simplified one by one

$=\sqrt{\frac{64x^5y^6}{x^7y^5} }$

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

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

Similarly for y,

$=\sqrt{\frac{64y^{(6-5)}}{x^{2}}}\\=\sqrt{\frac{64y}{x^{2}}}$

Applying the radical

$\sqrt{\frac{8^2*y}{x^{2}}}\\So\ the\ answer\ will\ be\\= \frac{8\sqrt{y}}{x}$

So, last option is the correct answer ..