Evaluate (-2/3)^4

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

Step 1

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

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

${(- 1)}^{4} {(\frac{2}{3})}^{4}$

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

${(- 1)}^{4} \frac{2^{4}}{3^{4}}$

Step 2

Raise $- 1$ to the power of $4$ .

$1 \frac{2^{4}}{3^{4}}$

Step 3

Multiply $\frac{2^{4}}{3^{4}}$ by $1$ .

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

Step 4

Raise $2$ to the power of $4$ .

$\frac{16}{3^{4}}$

Step 5

Raise $3$ to the power of $4$ .

$\frac{16}{81}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{16}{81}$

Decimal Form:

$0.19753086 \dots$