Finite Math Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 2

Simplify the numerator.

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Step 2.1

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

$\frac{729 {\sqrt{2}}^{3}}{2^{3}}$

Step 2.2

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

$\frac{729 \sqrt{2^{3}}}{2^{3}}$

Step 2.3

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

$\frac{729 \sqrt{8}}{2^{3}}$

Step 2.4

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

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Step 2.4.1

Factor $4$ out of $8$ .

$\frac{729 \sqrt{4 (2)}}{2^{3}}$

Step 2.4.2

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

$\frac{729 \sqrt{2^{2} \cdot 2}}{2^{3}}$

Step 2.5

Pull terms out from under the radical.

$\frac{729 \cdot 2 \sqrt{2}}{2^{3}}$

Step 2.6

Multiply $729$ by $2$ .

$\frac{1458 \sqrt{2}}{2^{3}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

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

$\frac{1458 \sqrt{2}}{8}$

Step 3.2

Cancel the common factor of $1458$ and $8$ .

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Step 3.2.1

Factor $2$ out of $1458 \sqrt{2}$ .

$\frac{2 (729 \sqrt{2})}{8}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $2$ out of $8$ .

$\frac{2 (729 \sqrt{2})}{2 (4)}$

Step 3.2.2.2

Cancel the common factor.

$\frac{2 (729 \sqrt{2})}{2 \cdot 4}$

Step 3.2.2.3

Rewrite the expression.

$\frac{729 \sqrt{2}}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{729 \sqrt{2}}{4}$

Decimal Form:

$257.74042174 \dots$