What is e^{-1.007*10^{-4}*5000} ?

The solution to e^{-1.007*10^{-4}*5000} is 0.60441…

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simplify e^{-1.00710^{-4}5000}

simplify

e^{- 1.007 \cdot 1 0^{- 4} \cdot 5000}

0.60441 \dots

Solution steps

e^{- 1.007 \cdot 1 0^{- 4} \cdot 5000}

Apply exponent rule:

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

= \frac{1}{e ^{1 0^{- 4} \cdot 5000 \cdot 1.007}}

Multiply the numbers:

1.007 \cdot 5000 = 5035

= \frac{1}{e ^{1 0^{- 4} \cdot 5035}}

e^{5035 \cdot 1 0^{- 4}} = e^{\frac{1007}{2000}}

= \frac{1}{e ^{\frac{1007}{2000}}}

Convert element to a decimal form

e^{\frac{1007}{2000}} = 1.65450 \dots

= \frac{1}{1.65450 \dots}

Divide the numbers:

\frac{1}{1.65450 \dots} = 0.60441 \dots

= 0.60441 \dots

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What is e^{-1.007*10^{-4}*5000} ?
The solution to e^{-1.007*10^{-4}*5000} is 0.60441…