Calculus Examples

$f (4) = \frac{3}{256} x^{2} + x^{- 2}$

Step 1

Replace the variable $x$ with $4$ in the expression.

$f (4) = \frac{3}{256} \cdot {(4)}^{2} + {(4)}^{- 2}$

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

Raise $4$ to the power of $2$ .

$f (4) = \frac{3}{256} \cdot 16 + {(4)}^{- 2}$

Step 2.1.2

Cancel the common factor of $16$ .

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Step 2.1.2.1

Factor $16$ out of $256$ .

$f (4) = \frac{3}{16 (16)} \cdot 16 + {(4)}^{- 2}$

Step 2.1.2.2

Cancel the common factor.

$f (4) = \frac{3}{16 \cdot 16} \cdot 16 + {(4)}^{- 2}$

Step 2.1.2.3

Rewrite the expression.

$f (4) = \frac{3}{16} + {(4)}^{- 2}$

Step 2.1.3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$f (4) = \frac{3}{16} + \frac{1}{4^{2}}$

Step 2.1.4

Raise $4$ to the power of $2$ .

$f (4) = \frac{3}{16} + \frac{1}{16}$

Step 2.2

Simplify terms.

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Step 2.2.1

Combine the numerators over the common denominator.

$f (4) = \frac{3 + 1}{16}$

Step 2.2.2

Add $3$ and $1$ .

$f (4) = \frac{4}{16}$

Step 2.2.3

Cancel the common factor of $4$ and $16$ .

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Step 2.2.3.1

Factor $4$ out of $4$ .

$f (4) = \frac{4 (1)}{16}$

Step 2.2.3.2

Cancel the common factors.

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Step 2.2.3.2.1

Factor $4$ out of $16$ .

$f (4) = \frac{4 \cdot 1}{4 \cdot 4}$

Step 2.2.3.2.2

Cancel the common factor.

$f (4) = \frac{4 \cdot 1}{4 \cdot 4}$

Step 2.2.3.2.3

Rewrite the expression.

$f (4) = \frac{1}{4}$

Step 2.3

The final answer is $\frac{1}{4}$ .

$\frac{1}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$

Step 4