Simplify (3/(2^2))^-3

${(\frac{3}{2^{2}})}^{- 3}$

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

${(\frac{3}{4})}^{- 3}$

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{4}{3})}^{3}$

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

$\frac{4^{3}}{3^{3}}$

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

$\frac{64}{3^{3}}$

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

$\frac{64}{27}$

The result can be shown in multiple forms.

Exact Form:

$\frac{64}{27}$

Decimal Form:

$2.\overline{370}$

Mixed Number Form:

$2 \frac{10}{27}$