Simplify (p^3q)^-4

${(p^{3} q)}^{- 4}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Simplify the denominator.

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

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

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

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

$\frac{1}{p^{3 \cdot 4} q^{4}}$

Multiply $3$ by $4$ .

$\frac{1}{p^{12} q^{4}}$