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

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

Move ${(3 a)}^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Apply the product rule to $3 a$ .

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

Multiply $3$ by $3^{3}$ by adding the exponents.

Move $3^{3}$ .

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

Multiply $3^{3}$ by $3$ .

Raise $3$ to the power of $1$ .

$3^{3} \cdot 3^{1} a^{3}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3^{3 + 1} a^{3}$

Add $3$ and $1$ .

$3^{4} a^{3}$

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

$81 a^{3}$