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

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

Step 1

Raise $2$ to the power of $3$ .

${(- \frac{3}{8})}^{- 2}$

Step 2

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

${(- \frac{8}{3})}^{2}$

Step 3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{8}{3}$ .

${(- 1)}^{2} {(\frac{8}{3})}^{2}$

Apply the product rule to $\frac{8}{3}$ .

${(- 1)}^{2} \frac{8^{2}}{3^{2}}$

Step 4

Raise $- 1$ to the power of $2$ .

$1 \frac{8^{2}}{3^{2}}$

Step 5

Multiply $\frac{8^{2}}{3^{2}}$ by $1$ .

$\frac{8^{2}}{3^{2}}$

Step 6

Raise $8$ to the power of $2$ .

$\frac{64}{3^{2}}$

Step 7

Raise $3$ to the power of $2$ .

$\frac{64}{9}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{64}{9}$

Decimal Form:

$7.\overline{1}$

Mixed Number Form:

$7 \frac{1}{9}$