Simplify (3a^-3)^3

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

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

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

Combine $3$ and $\frac{1}{a^{3}}$ .

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

Simplify the expression.

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

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

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

$\frac{27}{{(a^{3})}^{3}}$

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

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

$\frac{27}{a^{3 \cdot 3}}$

Multiply $3$ by $3$ .

$\frac{27}{a^{9}}$

Simplify (3a^-3)^3

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