Question

Simplify. In the form of a paragraph, explain in complete sentences the steps necessary to simplify the expression and include the final answer in your explanation. Complete your work in the space provided.

(x^3y over xy^2) ^-2

Answer 1

y^2/x^4

Explanation:

Description

The fraction inside parentheses can be simplified by using the rule that an exponent in the denominator is the same as the opposite of that exponent in the numerator. Then factors with the same base can be combined by adding their exponents. Parentheses are eliminated by multiplying each exponent by the one outside the parentheses. Then any factors with negative exponents can be replaced by ones in the denominator with the opposite exponent.

Work

`\left((x^3y)/(xy^2)\right)^(-2)=(x^3yx^(-1)y{-2})^(-2)=(x^(3-1)y^(1-2))^(-2)\\\\=(x^2y^(-1))^(-2)=x^(2(-2))y^((-1)(-2))=x^(-4)y^2\\\\=\boxed{(y^2)/(x^4)}`