Find the Product (xy^-6)^2

${(x y^{- 6})}^{2}$

Step 1

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

${(x \frac{1}{y^{6}})}^{2}$

Step 2

Combine $x$ and $\frac{1}{y^{6}}$ .

${(\frac{x}{y^{6}})}^{2}$

Step 3

Apply basic rules of exponents.

Apply the product rule to $\frac{x}{y^{6}}$ .

$\frac{x^{2}}{{(y^{6})}^{2}}$

Multiply the exponents in ${(y^{6})}^{2}$ .

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

$\frac{x^{2}}{y^{6 \cdot 2}}$

Multiply $6$ by $2$ .

$\frac{x^{2}}{y^{12}}$