Algebra Examples

${(- 4 d^{0} \cdot 2^{- 3} \cdot e^{5})}^{- 1}$

Step 1

Anything raised to $0$ is $1$ .

${(- 4 \cdot 1 \cdot 2^{- 3} \cdot e^{5})}^{- 1}$

Step 2

Multiply $- 4$ by $1$ .

${(- 4 \cdot 2^{- 3} \cdot e^{5})}^{- 1}$

Step 3

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

${(- 4 \cdot \frac{1}{2^{3}} \cdot e^{5})}^{- 1}$

Step 4

Raise $2$ to the power of $3$ .

${(- 4 \cdot \frac{1}{8} \cdot e^{5})}^{- 1}$

Step 5

Cancel the common factor of $4$ .

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Step 5.1

Factor $4$ out of $- 4$ .

${(4 (- 1) \cdot \frac{1}{8} \cdot e^{5})}^{- 1}$

Step 5.2

Factor $4$ out of $8$ .

${(4 \cdot - 1 \cdot \frac{1}{4 \cdot 2} \cdot e^{5})}^{- 1}$

Step 5.3

Cancel the common factor.

${(4 \cdot - 1 \cdot \frac{1}{4 \cdot 2} \cdot e^{5})}^{- 1}$

Step 5.4

Rewrite the expression.

${(- 1 \cdot \frac{1}{2} \cdot e^{5})}^{- 1}$

Step 6

Rewrite $- 1 (\frac{1}{2})$ as $- (\frac{1}{2})$ .

${(- (\frac{1}{2}) \cdot e^{5})}^{- 1}$

Step 7

Combine $e^{5}$ and $\frac{1}{2}$ .

${(- \frac{e^{5}}{2})}^{- 1}$

Step 8

Change the sign of the exponent by rewriting the base as its reciprocal.

$- \frac{2}{e^{5}}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{2}{e^{5}}$

Decimal Form:

$- 0.01347589 \dots$