What is ((e^7)/(e^4))^{-1} ?

The solution to ((e^7)/(e^4))^{-1} is 1/(e^3)

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simplify ((e^7)/(e^4))^{-1}

simplify

(\frac{e ^{7}}{e ^{4}})^{- 1}

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

Decimal

0.04978 \dots

Solution steps

(\frac{e ^{7}}{e ^{4}})^{- 1}

Apply exponent rule:

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

= \frac{1}{( \frac{e ^{7}}{e ^{4}} )}

Apply the fraction rule:

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

= \frac{e ^{4}}{e ^{7}}

Apply exponent rule:

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

\frac{e ^{4}}{e ^{7}} = \frac{1}{e ^{7 - 4}}

= \frac{1}{e ^{7 - 4}}

Subtract the numbers:

7 - 4 = 3

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

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