What is ((e^5)/(e^2))^{-1} ?

The solution to ((e^5)/(e^2))^{-1} is 1/(e^3)

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simplify ((e^5)/(e^2))^{-1}

simplify

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

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

Decimal Notation

0.04978 \dots

Solution steps

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

Apply exponent rule:

a^{- 1} = \frac{1}{a}

= \frac{1}{( \frac{e ^{5}}{e ^{2}} )}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{e ^{2}}{e ^{5}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{e ^{2}}{e ^{5}} = \frac{1}{e ^{5 - 2}}

= \frac{1}{e ^{5 - 2}}

Subtract the numbers:

5 - 2 = 3

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

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

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