Question

Which expression is equivalent to sqrt128x^5y^6/2x^7y^5 ? Assume x 0 and y > 0.

Answer 1

Answer:

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

Step-by-step explanation:

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

we have division inside the square root .

LEts simplify it

128 divide by 2 is 64

use property of exponents to simplify the exponents

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

$\frac{x^5}{x^7} =x^{5-7}=x^{-2}$

$\frac{y^6}{y^5} =y^{6-5}=y$

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

$\sqrt{\frac{64x^{-2}y}{1}}$

To make the exponent positive move x to the denominator

$\sqrt{\frac{64y}{x^2}}$

Now we take square root

square root (64) is 8

square root of x^2 is x

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

Answer 2

Answer:

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

Step-by-step explanation:

We are given the following expression and we are to simplify it:

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

To make it easier to solve, we can also write this expression as:

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

Now we will cancel out the like terms to get:

$\sqrt {64*\frac{1} {x^2}*y }$

Taking the square root of the terms to get:

$8*\frac {1}{x} .\sqrt{y}$

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