Simplify ((-3p^-3)/(q^-4))^2

${(\frac{- 3 p^{- 3}}{q^{- 4}})}^{2}$

Move $p^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{- 3}{q^{- 4} p^{3}})}^{2}$

Move $q^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{- 3 q^{4}}{p^{3}})}^{2}$

Move the negative in front of the fraction.

${(- \frac{(3) q^{4}}{p^{3}})}^{2}$

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

Apply the product rule to $- \frac{3 q^{4}}{p^{3}}$ .

${(- 1)}^{2} {(\frac{3 q^{4}}{p^{3}})}^{2}$

Apply the product rule to $\frac{3 q^{4}}{p^{3}}$ .

${(- 1)}^{2} \frac{{(3 q^{4})}^{2}}{{(p^{3})}^{2}}$

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

${(- 1)}^{2} \frac{3^{2} {(q^{4})}^{2}}{{(p^{3})}^{2}}$

Simplify the expression.

Raise $- 1$ to the power of $2$ .

$1 \frac{3^{2} {(q^{4})}^{2}}{{(p^{3})}^{2}}$

Multiply $\frac{3^{2} {(q^{4})}^{2}}{{(p^{3})}^{2}}$ by $1$ .

$\frac{3^{2} {(q^{4})}^{2}}{{(p^{3})}^{2}}$

Simplify the numerator.

Raise $3$ to the power of $2$ .

$\frac{9 {(q^{4})}^{2}}{{(p^{3})}^{2}}$

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

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

$\frac{9 q^{4 \cdot 2}}{{(p^{3})}^{2}}$

Multiply $4$ by $2$ .

$\frac{9 q^{8}}{{(p^{3})}^{2}}$

Multiply the exponents in ${(p^{3})}^{2}$ .

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

$\frac{9 q^{8}}{p^{3 \cdot 2}}$

Multiply $3$ by $2$ .

$\frac{9 q^{8}}{p^{6}}$