Evaluate ((2/3)^2)^3

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

Step 1

Multiply the exponents in ${({(\frac{2}{3})}^{2})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Multiply $2$ by $3$ .

${(\frac{2}{3})}^{6}$

Step 2

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

$\frac{2^{6}}{3^{6}}$

Step 3

Raise $2$ to the power of $6$ .

$\frac{64}{3^{6}}$

Step 4

Raise $3$ to the power of $6$ .

$\frac{64}{729}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{64}{729}$

Decimal Form:

$0.08779149 \dots$