What is e^{(-2000\times 0.4\times 10^{-3})} ?

The solution to e^{(-2000\times 0.4\times 10^{-3})} is 0.44932…

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simplify e^{(-2000\times 0.4\times 10^{-3})}

simplify

e^{(- 2000 \cdot 0.4 \cdot 1 0^{- 3})}

0.44932 \dots

Solution steps

e^{(- 2000 \cdot 0.4 \cdot 1 0^{- 3})}

Apply exponent rule:

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

= \frac{1}{e ^{1 0^{- 3} \cdot 2000 \cdot 0.4}}

Multiply the numbers:

2000 \cdot 0.4 = 800

= \frac{1}{e ^{1 0^{- 3} \cdot 800}}

e^{800 \cdot 1 0^{- 3}} = e^{\frac{4}{5}}

= \frac{1}{e ^{\frac{4}{5}}}

Convert element to a decimal form

e^{\frac{4}{5}} = 2.22554 \dots

= \frac{1}{2.22554 \dots}

Divide the numbers:

\frac{1}{2.22554 \dots} = 0.44932 \dots

= 0.44932 \dots

e^{- xx}

(\frac{6}{7})^{3} \cdot (\frac{6}{7})^{8}

5.5 \cdot 1 0^{- 4}

5.5 \cdot 1 0^{- 7}

What is e^{(-2000\times 0.4\times 10^{-3})} ?
The solution to e^{(-2000\times 0.4\times 10^{-3})} is 0.44932…