Basic Math Examples

${(\frac{\sqrt{2}}{9})}^{3}$

Step 1

Apply the product rule to $\frac{\sqrt{2}}{9}$ .

$\frac{{\sqrt{2}}^{3}}{9^{3}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite ${\sqrt{2}}^{3}$ as $\sqrt{2^{3}}$ .

$\frac{\sqrt{2^{3}}}{9^{3}}$

Step 2.2

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

$\frac{\sqrt{8}}{9^{3}}$

Step 2.3

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

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Step 2.3.1

Factor $4$ out of $8$ .

$\frac{\sqrt{4 (2)}}{9^{3}}$

Step 2.3.2

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

$\frac{\sqrt{2^{2} \cdot 2}}{9^{3}}$

$\frac{\sqrt{2^{2} \cdot 2}}{9^{3}}$

Step 2.4

Pull terms out from under the radical.

$\frac{2 \sqrt{2}}{9^{3}}$

$\frac{2 \sqrt{2}}{9^{3}}$

Step 3

Raise $9$ to the power of $3$ .

$\frac{2 \sqrt{2}}{729}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{2 \sqrt{2}}{729}$

Decimal Form:

$0.00387987 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$