Evaluate (x^2y^-1)^2

${(x^{2} y^{- 1})}^{2}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(x^{2} \frac{1}{y})}^{2}$

Step 2

Combine $x^{2}$ and $\frac{1}{y}$ .

${(\frac{x^{2}}{y})}^{2}$

Step 3

Apply basic rules of exponents.

Apply the product rule to $\frac{x^{2}}{y}$ .

$\frac{{(x^{2})}^{2}}{y^{2}}$

Multiply the exponents in ${(x^{2})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{x^{2 \cdot 2}}{y^{2}}$

Multiply $2$ by $2$ .

$\frac{x^{4}}{y^{2}}$