Simplify (x^-1*y^2)^3

${(x^{- 1} \cdot y^{2})}^{3}$

Step 1

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

${(\frac{1}{x} \cdot y^{2})}^{3}$

Step 2

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

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

Step 3

Apply basic rules of exponents.

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

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

Multiply the exponents in ${(y^{2})}^{3}$ .

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

$\frac{y^{2 \cdot 3}}{x^{3}}$

Multiply $2$ by $3$ .

$\frac{y^{6}}{x^{3}}$