Algebra Examples

${(\frac{\sqrt{8}}{3})}^{2}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.1.1

Factor $4$ out of $8$ .

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

Step 1.1.2

Rewrite $4$ as $2^{2}$ .

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

Step 1.2

Pull terms out from under the radical.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 3

Simplify the numerator.

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Step 3.1

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

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.2.3

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

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

Step 3.2.4

Cancel the common factor of $2$ .

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Step 3.2.4.1

Cancel the common factor.

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

Step 3.2.4.2

Rewrite the expression.

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

Step 3.2.5

Evaluate the exponent.

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

Step 4

Simplify the expression.

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Step 4.1

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

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

Step 4.2

Multiply $4$ by $2$ .

$\frac{8}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{9}$

Decimal Form:

$0.\overline{8}$