Calculus Examples

$h (4) = (s^{- \frac{1}{2}} + 2 s) (7 - s^{- 1})$

Step 1

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

$h (4) = ({(4)}^{- \frac{1}{2}} + 2 (4)) (7 - {(4)}^{- 1})$

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$h (4) = (\frac{1}{4^{\frac{1}{2}}} + 2 (4)) (7 - {(4)}^{- 1})$

Step 2.1.2

Simplify the denominator.

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Step 2.1.2.1

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

$h (4) = (\frac{1}{{(2^{2})}^{\frac{1}{2}}} + 2 (4)) (7 - {(4)}^{- 1})$

Step 2.1.2.2

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

$h (4) = (\frac{1}{2^{2 (\frac{1}{2})}} + 2 (4)) (7 - {(4)}^{- 1})$

Step 2.1.2.3

Cancel the common factor of $2$ .

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Step 2.1.2.3.1

Cancel the common factor.

$h (4) = (\frac{1}{2^{2 (\frac{1}{2})}} + 2 (4)) (7 - {(4)}^{- 1})$

Step 2.1.2.3.2

Rewrite the expression.

$h (4) = (\frac{1}{2} + 2 (4)) (7 - {(4)}^{- 1})$

Step 2.1.2.4

Evaluate the exponent.

$h (4) = (\frac{1}{2} + 2 (4)) (7 - {(4)}^{- 1})$

Step 2.1.3

Multiply $2$ by $4$ .

$h (4) = (\frac{1}{2} + 8) (7 - {(4)}^{- 1})$

Step 2.2

To write $8$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$h (4) = (\frac{1}{2} + 8 \cdot \frac{2}{2}) (7 - {(4)}^{- 1})$

Step 2.3

Combine $8$ and $\frac{2}{2}$ .

$h (4) = (\frac{1}{2} + \frac{8 \cdot 2}{2}) (7 - {(4)}^{- 1})$

Step 2.4

Combine the numerators over the common denominator.

$h (4) = \frac{1 + 8 \cdot 2}{2} \cdot (7 - {(4)}^{- 1})$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $8$ by $2$ .

$h (4) = \frac{1 + 16}{2} \cdot (7 - {(4)}^{- 1})$

Step 2.5.2

Add $1$ and $16$ .

$h (4) = \frac{17}{2} \cdot (7 - {(4)}^{- 1})$

Step 2.6

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

$h (4) = \frac{17}{2} \cdot (7 - \frac{1}{4})$

Step 2.7

To write $7$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$h (4) = \frac{17}{2} \cdot (7 \cdot \frac{4}{4} - \frac{1}{4})$

Step 2.8

Combine $7$ and $\frac{4}{4}$ .

$h (4) = \frac{17}{2} \cdot (\frac{7 \cdot 4}{4} - \frac{1}{4})$

Step 2.9

Combine the numerators over the common denominator.

$h (4) = \frac{17}{2} \cdot \frac{7 \cdot 4 - 1}{4}$

Step 2.10

Simplify the numerator.

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Step 2.10.1

Multiply $7$ by $4$ .

$h (4) = \frac{17}{2} \cdot \frac{28 - 1}{4}$

Step 2.10.2

Subtract $1$ from $28$ .

$h (4) = \frac{17}{2} \cdot \frac{27}{4}$

Step 2.11

Multiply $\frac{17}{2} \cdot \frac{27}{4}$ .

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Step 2.11.1

Multiply $\frac{17}{2}$ by $\frac{27}{4}$ .

$h (4) = \frac{17 \cdot 27}{2 \cdot 4}$

Step 2.11.2

Multiply $17$ by $27$ .

$h (4) = \frac{459}{2 \cdot 4}$

Step 2.11.3

Multiply $2$ by $4$ .

$h (4) = \frac{459}{8}$

Step 2.12

The final answer is $\frac{459}{8}$ .

$\frac{459}{8}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{459}{8}$

Decimal Form:

$57.375$

Mixed Number Form:

$57 \frac{3}{8}$

Step 4