What is 0.2e^{-200*0.006} ?

The solution to 0.2e^{-200*0.006} is 0.06023…

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simplify 0.2e^{-200*0.006}

simplify

0.2 e^{- 200 \cdot 0.006}

0.06023 \dots

Solution steps

0.2 e^{- 200 \cdot 0.006}

Apply exponent rule:

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

= 0.2 \cdot \frac{1}{e ^{200 \cdot 0.006}}

Multiply the numbers:

200 \cdot 0.006 = 1.2

= 0.2 \cdot \frac{1}{e ^{1.2}}

Multiply fractions:

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

= \frac{1 \cdot 0.2}{e ^{1.2}}

Multiply the numbers:

1 \cdot 0.2 = 0.2

= \frac{0.2}{e ^{1.2}}

e^{1.2} = 3.32011 \dots

= \frac{0.2}{3.32011 \dots}

Divide the numbers:

\frac{0.2}{3.32011 \dots} = 0.06023 \dots

= 0.06023 \dots

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

5.56 \cdot 1 0^{- 6} \cdot 3600

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