Simplify ((x^-2y)/(z^2))^-4

${(\frac{x^{- 2} y}{z^{2}})}^{- 4}$

Step 1

Move $x^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{y}{z^{2} x^{2}})}^{- 4}$

Step 2

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{z^{2} x^{2}}{y})}^{4}$

Step 3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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

$\frac{{(z^{2} x^{2})}^{4}}{y^{4}}$

Apply the product rule to $z^{2} x^{2}$ .

$\frac{{(z^{2})}^{4} {(x^{2})}^{4}}{y^{4}}$

Step 4

Simplify the numerator.

Multiply the exponents in ${(z^{2})}^{4}$ .

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

$\frac{z^{2 \cdot 4} {(x^{2})}^{4}}{y^{4}}$

Multiply $2$ by $4$ .

$\frac{z^{8} {(x^{2})}^{4}}{y^{4}}$

Multiply the exponents in ${(x^{2})}^{4}$ .

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

$\frac{z^{8} x^{2 \cdot 4}}{y^{4}}$

Multiply $2$ by $4$ .

$\frac{z^{8} x^{8}}{y^{4}}$