Evaluate -2(3/2)^-2

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

$- 2 (\frac{4}{9})$

Step 5

Multiply $- 2 (\frac{4}{9})$ .

Combine $- 2$ and $\frac{4}{9}$ .

$\frac{- 2 \cdot 4}{9}$

Multiply $- 2$ by $4$ .

$\frac{- 8}{9}$

Step 6

Move the negative in front of the fraction.

$- \frac{8}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{8}{9}$

Decimal Form:

$- 0.\overline{8}$