Simplify (-2/3)^-2

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

Step 1

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

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

Step 2

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

Apply the product rule to $- \frac{3}{2}$ .

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

Apply the product rule to $\frac{3}{2}$ .

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

Step 3

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

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

Step 4

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

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

Step 5

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

$\frac{9}{2^{2}}$

Step 6

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

$\frac{9}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{4}$

Decimal Form:

$2.25$

Mixed Number Form:

$2 \frac{1}{4}$