Calculus Examples

$f (2) = - 12 {(4 \cdot 2 + 4)}^{- 4}$

Step 1

Multiply $4$ by $2$ .

$f (2) = - 12 {(8 + 4)}^{- 4}$

Step 2

Add $8$ and $4$ .

$f (2) = - 12 \cdot 12^{- 4}$

Step 3

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

$f (2) = - 12 \cdot \frac{1}{12^{4}}$

Step 4

Raise $12$ to the power of $4$ .

$f (2) = - 12 \cdot \frac{1}{20736}$

Step 5

Cancel the common factor of $12$ .

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Step 5.1

Factor $12$ out of $- 12$ .

$f (2) = 12 (- 1) \cdot \frac{1}{20736}$

Step 5.2

Factor $12$ out of $20736$ .

$f (2) = 12 \cdot - 1 \cdot \frac{1}{12 \cdot 1728}$

Step 5.3

Cancel the common factor.

$f (2) = 12 \cdot - 1 \cdot \frac{1}{12 \cdot 1728}$

Step 5.4

Rewrite the expression.

$f (2) = - 1 \cdot \frac{1}{1728}$

Step 6

Rewrite $- 1 (\frac{1}{1728})$ as $- (\frac{1}{1728})$ .

$f (2) = - \frac{1}{1728}$