Evaluate ((2 square root of 2)/3)^2

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

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

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

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

Apply the product rule to $2 \sqrt{2}$ .

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

Simplify the numerator.

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

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

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

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

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

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

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Simplify the expression.

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

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

Multiply $4$ by $2$ .

$\frac{8}{9}$

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{9}$

Decimal Form:

$0.\overline{8}$