What is 5e^{-8}*(-2e^3)^2 ?

The solution to 5e^{-8}*(-2e^3)^2 is (20)/(e^2)

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simplify 5e^{-8}*(-2e^3)^2

simplify

5 e^{- 8} \cdot (- 2 e^{3})^{2}

\frac{20}{e ^{2}}

Decimal Notation

2.70670 \dots

Solution steps

5 e^{- 8} (- 2 e^{3})^{2}

Apply exponent rule:

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

= 5 \cdot \frac{1}{e ^{8}} (- 2 e^{3})^{2}

(- 2 e^{3})^{2} = 2^{2} e^{6}

= 2^{2} \cdot 5 e^{6} \frac{1}{e ^{8}}

Multiply fractions:

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

= \frac{1 \cdot 5 \cdot 2 ^{2} e ^{6}}{e ^{8}}

Multiply the numbers:

1 \cdot 5 = 5

= \frac{2 ^{2} \cdot 5 e ^{6}}{e ^{8}}

Apply exponent rule:

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

\frac{e ^{6}}{e ^{8}} = \frac{1}{e ^{8 - 6}}

= \frac{2 ^{2} \cdot 5}{e ^{8 - 6}}

Subtract the numbers:

8 - 6 = 2

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

2^{2} \cdot 5 = 20

= \frac{20}{e ^{2}}

0.23 5^{- \frac{1}{6}} \cdot 28

e^{- l n ∣ 1 + x ∣}

e^{- 2 \cdot 0.05}

(e^{t^{2}}) (e^{t})