Simplify (4a^2)^-3

${(4 a^{2})}^{- 3}$

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

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

Simplify the denominator.

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Apply the product rule to $4 a^{2}$ .

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

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

$\frac{1}{64 {(a^{2})}^{3}}$

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

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

$\frac{1}{64 a^{2 \cdot 3}}$

Multiply $2$ by $3$ .

$\frac{1}{64 a^{6}}$

Simplify (4a^2)^-3