What is 500*e^{-0.25*10} ?

The solution to 500*e^{-0.25*10} is 41.04249…

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simplify 500e^{-0.2510}

simplify

500 \cdot e^{- 0.25 \cdot 10}

41.04249 \dots

Solution steps

500 e^{- 0.25 \cdot 10}

Apply exponent rule:

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

= 500 \cdot \frac{1}{e ^{10 \cdot 0.25}}

Multiply the numbers:

0.25 \cdot 10 = 2.5

= 500 \cdot \frac{1}{e ^{2.5}}

Multiply fractions:

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

= \frac{1 \cdot 500}{e ^{2.5}}

Multiply the numbers:

1 \cdot 500 = 500

= \frac{500}{e ^{2.5}}

e^{2.5} = 12.18249 \dots

= \frac{500}{12.18249 \dots}

Divide the numbers:

\frac{500}{12.18249 \dots} = 41.04249 \dots

= 41.04249 \dots

- 3 a^{6} b^{2} (2 a^{5} b^{7})

(- 5)^{2}

(3.7 \cdot 1 0^{- 8}) (2.9 \cdot 1 0^{6})

40 \cdot 1 0^{- 3} \cdot \frac{1000}{1.3 \cdot 1 0 ^{- 3}}