Calculus Examples

$f (0) = \frac{64}{{(x^{2} + 64)}^{\frac{3}{2}}}$

Step 1

Replace the variable $x$ with $0$ in the expression.

$f (0) = \frac{64}{{({(0)}^{2} + 64)}^{\frac{3}{2}}}$

Step 2

Simplify the result.

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Step 2.1

Simplify the denominator.

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Step 2.1.1

Raising $0$ to any positive power yields $0$ .

$f (0) = \frac{64}{{(0 + 64)}^{\frac{3}{2}}}$

Step 2.1.2

Add $0$ and $64$ .

$f (0) = \frac{64}{64^{\frac{3}{2}}}$

Step 2.1.3

Rewrite $64$ as $8^{2}$ .

$f (0) = \frac{64}{{(8^{2})}^{\frac{3}{2}}}$

Step 2.1.4

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

$f (0) = \frac{64}{8^{2 (\frac{3}{2})}}$

Step 2.1.5

Cancel the common factor of $2$ .

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Step 2.1.5.1

Cancel the common factor.

$f (0) = \frac{64}{8^{2 (\frac{3}{2})}}$

Step 2.1.5.2

Rewrite the expression.

$f (0) = \frac{64}{8^{3}}$

Step 2.1.6

Raise $8$ to the power of $3$ .

$f (0) = \frac{64}{512}$

Step 2.2

Cancel the common factor of $64$ and $512$ .

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Step 2.2.1

Factor $64$ out of $64$ .

$f (0) = \frac{64 (1)}{512}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $64$ out of $512$ .

$f (0) = \frac{64 \cdot 1}{64 \cdot 8}$

Step 2.2.2.2

Cancel the common factor.

$f (0) = \frac{64 \cdot 1}{64 \cdot 8}$

Step 2.2.2.3

Rewrite the expression.

$f (0) = \frac{1}{8}$

Step 2.3

The final answer is $\frac{1}{8}$ .

$\frac{1}{8}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{8}$

Decimal Form:

$0.125$

Step 4