What is ((e^{-2})^{7/2})^{-2} ?

The solution to ((e^{-2})^{7/2})^{-2} is e^{14}

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simplify ((e^{-2})^{7/2})^{-2}

simplify

((e^{- 2})^{\frac{7}{2}})^{- 2}

e^{14}

Decimal Notation

1202604.28416 \dots

Solution steps

((e^{- 2})^{\frac{7}{2}})^{- 2}

(e^{- 2})^{\frac{7}{2}} : e^{- 7}

= (e^{- 7})^{- 2}

Apply exponent rule:

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

= \frac{1}{( e ^{- 7} ) ^{2}}

(e^{- 7})^{2} : e^{- 14}

= \frac{1}{e ^{- 14}}

Apply exponent rule:

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

e^{- 14} = \frac{1}{e ^{14}}

= \frac{1}{\frac{1}{e ^{14}}}

Apply the fraction rule:

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

= \frac{e ^{14}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= e^{14}

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