Basic Math Examples

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

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

Step 1

Apply the product rule to

\frac{\sqrt{2}}{9}

$\frac{\sqrt{2}}{9}$ .

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

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

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Rewrite

{\sqrt{2}}^{3}

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

\sqrt{2^{3}}

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

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

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

Step 2.2

Raise

2

$2$ to the power of

3

$3$ .

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

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

Step 2.3

Rewrite

8

$8$ as

2^{2} \cdot 2

$2^{2} \cdot 2$ .

Tap for more steps...

Step 2.3.1

Factor

4

$4$ out of

8

$8$ .

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

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

Step 2.3.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

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

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

\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}}

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

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

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

Step 3

Raise

9

$9$ to the power of

3

$3$ .

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

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

Decimal Form:

0.00387987 \dots

$0.00387987 \dots$

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

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