Precalculus Examples

$2 - 8 e^{- 2 \ln (2)}$

Step 1

Simplify each term.

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Step 1.1

Simplify $- 2 \ln (2)$ by moving $- 2$ inside the logarithm.

$2 - 8 e^{\ln (2^{- 2})}$

Step 1.2

Exponentiation and log are inverse functions.

$2 - 8 \cdot 2^{- 2}$

Step 1.3

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

$2 - 8 \cdot \frac{1}{2^{2}}$

Step 1.4

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

$2 - 8 \cdot \frac{1}{4}$

Step 1.5

Cancel the common factor of $4$ .

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Step 1.5.1

Factor $4$ out of $- 8$ .

$2 + 4 (- 2) \cdot \frac{1}{4}$

Step 1.5.2

Cancel the common factor.

$2 + 4 \cdot - 2 \cdot \frac{1}{4}$

Step 1.5.3

Rewrite the expression.

$2 - 2$

Step 2

Subtract $2$ from $2$ .

$0$