Simplify (3/2)^-2

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

Step 1

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

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

Step 2

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

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

Step 3

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

$\frac{4}{3^{2}}$

Step 4

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

$\frac{4}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{9}$

Decimal Form:

$0.\overline{4}$