Simplify ((3x^2)/y)^-4

${(\frac{3 x^{2}}{y})}^{- 4}$

Step 1

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

${(\frac{y}{3 x^{2}})}^{4}$

Step 2

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

Apply the product rule to $\frac{y}{3 x^{2}}$ .

$\frac{y^{4}}{{(3 x^{2})}^{4}}$

Apply the product rule to $3 x^{2}$ .

$\frac{y^{4}}{3^{4} {(x^{2})}^{4}}$

Step 3

Simplify the denominator.

Raise $3$ to the power of $4$ .

$\frac{y^{4}}{81 {(x^{2})}^{4}}$

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

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

$\frac{y^{4}}{81 x^{2 \cdot 4}}$

Multiply $2$ by $4$ .

$\frac{y^{4}}{81 x^{8}}$