What is 1500*e^{-2000*(1/240-1/289)} ?

The solution to 1500*e^{-2000*(1/240-1/289)} is (1500)/(e^{1225/867)}

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simplify 1500e^{-2000(1/240-1/289)}

simplify

1500 \cdot e^{- 2000 \cdot (\frac{1}{240} - \frac{1}{289})}

\frac{1500}{e ^{\frac{1225}{867}}}

Decimal Notation

365.14782 \dots

Solution steps

1500 e^{- 2000 (\frac{1}{240} - \frac{1}{289})}

Apply exponent rule:

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

= 1500 \cdot \frac{1}{e ^{2000 (\frac{1}{240} - \frac{1}{289})}}

\frac{1}{e ^{2000 (\frac{1}{240} - \frac{1}{289})}} = \frac{1}{e ^{2000 \cdot \frac{49}{69360}}}

= 1500 \cdot \frac{1}{e ^{2000 \cdot \frac{49}{69360}}}

Multiply fractions:

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

= \frac{1 \cdot 1500}{e ^{2000 \cdot \frac{49}{69360}}}

Multiply the numbers:

1 \cdot 1500 = 1500

= \frac{1500}{e ^{2000 \cdot \frac{49}{69360}}}

e^{2000 \cdot \frac{49}{69360}} = e^{\frac{1225}{867}}

= \frac{1500}{e ^{\frac{1225}{867}}}

e^{- 3.2} \cdot 3. 2^{2}

10 e^{- \frac{1}{2}}

9.99 \cdot 1 0^{- 3}

- 2.3 \cdot 1 0^{- 6}

What is 1500*e^{-2000*(1/240-1/289)} ?
The solution to 1500*e^{-2000*(1/240-1/289)} is (1500)/(e^{1225/867)}