Simplify (-(3a^3)/(b^3))^4

${(- \frac{3 a^{3}}{b^{3}})}^{4}$

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

Apply the product rule to $- \frac{3 a^{3}}{b^{3}}$ .

${(- 1)}^{4} {(\frac{3 a^{3}}{b^{3}})}^{4}$

Apply the product rule to $\frac{3 a^{3}}{b^{3}}$ .

${(- 1)}^{4} \frac{{(3 a^{3})}^{4}}{{(b^{3})}^{4}}$

Apply the product rule to $3 a^{3}$ .

${(- 1)}^{4} \frac{3^{4} {(a^{3})}^{4}}{{(b^{3})}^{4}}$

Simplify the expression.

Raise $- 1$ to the power of $4$ .

$1 \frac{3^{4} {(a^{3})}^{4}}{{(b^{3})}^{4}}$

Multiply $\frac{3^{4} {(a^{3})}^{4}}{{(b^{3})}^{4}}$ by $1$ .

$\frac{3^{4} {(a^{3})}^{4}}{{(b^{3})}^{4}}$

Simplify the numerator.

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

$\frac{81 {(a^{3})}^{4}}{{(b^{3})}^{4}}$

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

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

$\frac{81 a^{3 \cdot 4}}{{(b^{3})}^{4}}$

Multiply $3$ by $4$ .

$\frac{81 a^{12}}{{(b^{3})}^{4}}$

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

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

$\frac{81 a^{12}}{b^{3 \cdot 4}}$

Multiply $3$ by $4$ .

$\frac{81 a^{12}}{b^{12}}$