What is (-2e^3)e^{-2} ?

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

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simplify (-2e^3)e^{-2}

simplify

(- 2 e^{3}) e^{- 2}

- 2 e

Solution steps

(- 2 e^{3}) e^{- 2}

Apply exponent rule:

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

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

Remove parentheses:

(- a) = - a

= - 2 e^{3} \frac{1}{e ^{2}}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{1 \cdot 2 e ^{3}}{e ^{2}}

Multiply the numbers:

1 \cdot 2 = 2

= - \frac{2 e ^{3}}{e ^{2}}

Apply exponent rule:

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

\frac{e ^{3}}{e ^{2}} = e^{3 - 2}

= 2 e^{3 - 2}

Subtract the numbers:

3 - 2 = 1

= - 2 e

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