What is (15*10^{-12})(e^{(0.6)/(0.026)}-1)(25) ?

The solution to (15*10^{-12})(e^{(0.6)/(0.026)}-1)(25) is 3.94649…

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simplify (15*10^{-12})(e^{(0.6)/(0.026)}-1)(25)

simplify

(15 \cdot 1 0^{- 12}) (e^{\frac{0.6}{0.026}} - 1) (25)

3.94649 \dots

Solution steps

(15 \cdot 1 0^{- 12}) (e^{\frac{0.6}{0.026}} - 1) (25)

Apply exponent rule:

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

= 15 \cdot 25 \cdot \frac{1}{1 0 ^{12}} (e^{\frac{0.6}{0.026}} - 1)

Multiply fractions:

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

= \frac{1 \cdot 15 ( e ^{\frac{0.6}{0.026}} - 1 ) \cdot 25}{1 0 ^{12}}

Multiply the numbers:

1 \cdot 15 \cdot 25 = 375

= \frac{375 ( e ^{\frac{0.6}{0.026}} - 1 )}{1 0 ^{12}}

Factor

375 : 5^{3} \cdot 3

Factor

1 0^{12} : 2^{12} \cdot 5^{12}

= \frac{5 ^{3} \cdot 3 ( e ^{\frac{0.6}{0.026}} - 1 )}{2 ^{12} \cdot 5 ^{12}}

Cancel

\frac{3 \cdot 5 ^{3} ( e ^{\frac{0.6}{0.026}} - 1 )}{2 ^{12} \cdot 5 ^{12}} : \frac{3 ( e ^{\frac{0.6}{0.026}} - 1 )}{2 ^{12} \cdot 5 ^{9}}

= \frac{3 ( e ^{\frac{0.6}{0.026}} - 1 )}{2 ^{12} \cdot 5 ^{9}}

e^{\frac{0.6}{0.026}} = 10523988179.435293

= \frac{3 ( 10523988179.435293 - 1 )}{2 ^{12} \cdot 5 ^{9}}

3 (10523988179.435293 - 1) = 31571964535.30588

= \frac{31571964535.30588}{2 ^{12} \cdot 5 ^{9}}

2^{12} \cdot 5^{9} = 8000000000

= \frac{31571964535.30588}{8000000000}

Divide the numbers:

\frac{31571964535.30588}{8000000000} = 3.94649 \dots

= 3.94649 \dots

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What is (15*10^{-12})(e^{(0.6)/(0.026)}-1)(25) ?
The solution to (15*10^{-12})(e^{(0.6)/(0.026)}-1)(25) is 3.94649…