Find the Exact Value (-2/3)^2

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

Step 1

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

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

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

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

$\frac{4}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{9}$

Decimal Form:

$0.\overline{4}$