# How do you use the laws of exponents to simplify the expression ((4x^5y^2)/(-2x^3y^2))^2?

Apr 30, 2015

The answer is $4 {x}^{4}$.

Simplify ${\left(\frac{4 {x}^{5} {y}^{2}}{- 2 {x}^{3} {y}^{2}}\right)}^{2}$ .

Simplify what's inside the parentheses first.

Cancel the ${y}^{2}$ from the numerator and denominator.

${\left(\frac{4 {x}^{5} \cancel{{y}^{2}}}{- 2 {x}^{3} \cancel{{y}^{2}}}\right)}^{2}$

Divide $4$ in the numerator by $- 2$ in the denominator.

${\left(\frac{- 2 {x}^{5}}{{x}^{3}}\right)}^{2}$

Simplify the exponents by subtraction.

${\left(- 2 {x}^{5 - 3}\right)}^{2}$

Square the simplified term inside the parentheses.

${\left(- 2 {x}^{2}\right)}^{2} = 4 {x}^{4}$