Calculus Examples

$\frac{32}{{({(2)}^{2} + 32)}^{\frac{3}{2}}}$

Step 1

Simplify the denominator.

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Step 1.1

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

$\frac{32}{{(4 + 32)}^{\frac{3}{2}}}$

Step 1.2

Add $4$ and $32$ .

$\frac{32}{36^{\frac{3}{2}}}$

Step 1.3

Rewrite $36$ as $6^{2}$ .

$\frac{32}{{(6^{2})}^{\frac{3}{2}}}$

Step 1.4

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

$\frac{32}{6^{2 (\frac{3}{2})}}$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Cancel the common factor.

$\frac{32}{6^{2 (\frac{3}{2})}}$

Step 1.5.2

Rewrite the expression.

$\frac{32}{6^{3}}$

$\frac{32}{6^{3}}$

Step 1.6

Raise $6$ to the power of $3$ .

$\frac{32}{216}$

$\frac{32}{216}$

Step 2

Cancel the common factor of $32$ and $216$ .

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Step 2.1

Factor $8$ out of $32$ .

$\frac{8 (4)}{216}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $8$ out of $216$ .

$\frac{8 \cdot 4}{8 \cdot 27}$

Step 2.2.2

Cancel the common factor.

$\frac{8 \cdot 4}{8 \cdot 27}$

Step 2.2.3

Rewrite the expression.

$\frac{4}{27}$

$\frac{4}{27}$

$\frac{4}{27}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{27}$

Decimal Form:

$0.\overline{148}$

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