Question

Which expression is equivalent to 128x^5y^6 \ 2x^7y^5 ? Assume x > 0 and y > 0.

Answer 1

Answer: Last option.

Step-by-step explanation:

Given the expression:

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

The Quotient of powers property states that:

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

And the Power of a powet property states that:

$(a^m)^n=a^{mn}$

Then, applying these properties, you get:

$=\sqrt{\frac{(2^3)^26y}{x^2}$

Now you must remember that:

$\sqrt[a]{a^n}=a$

Therefore, simpliying the expression, you get:

$=\frac{2^3\sqrt{y}}{x}=\frac{8\sqrt{y}}{x}$

Answer 2

Answer:D

Step-by-step explanation: