Precalculus Examples

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

Step 1

Cancel the common factor of $e^{5}$ and $e^{2}$ .

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Step 1.1

Factor $e^{2}$ out of $e^{5}$ .

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

Multiply by $1$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

${(\frac{e^{3}}{1})}^{- 1}$

Step 1.2.4

Divide $e^{3}$ by $1$ .

${(e^{3})}^{- 1}$

Step 2

Multiply the exponents in ${(e^{3})}^{- 1}$ .

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Step 2.1

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

$e^{3 \cdot - 1}$

Step 2.2

Multiply $3$ by $- 1$ .

$e^{- 3}$

Step 3

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

$\frac{1}{e^{3}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{e^{3}}$

Decimal Form:

$0.04978706 \dots$