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

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

Step 1

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

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

Step 2

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

Apply the product rule to $\frac{y}{3 x^{4}}$ .

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

Apply the product rule to $3 x^{4}$ .

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

Step 3

Simplify the denominator.

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

$\frac{y^{3}}{27 {(x^{4})}^{3}}$

Multiply the exponents in ${(x^{4})}^{3}$ .

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

$\frac{y^{3}}{27 x^{4 \cdot 3}}$

Multiply $4$ by $3$ .

$\frac{y^{3}}{27 x^{12}}$