What is (32.1*10^3)e^{-2*(2.78*10^{-7})*600} ?

The solution to (32.1*10^3)e^{-2*(2.78*10^{-7})*600} is 32089.29322…

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simplify (32.110^3)e^{-2(2.7810^{-7})600}

simplify

(32.1 \cdot 1 0^{3}) e^{- 2 \cdot (2.78 \cdot 1 0^{- 7}) \cdot 600}

32089.29322 \dots

Solution steps

(32.1 \cdot 1 0^{3}) e^{- 2 (2.78 \cdot 1 0^{- 7}) \cdot 600}

Apply exponent rule:

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

= 1 0^{3} \cdot 32.1 \cdot \frac{1}{e ^{1 0^{- 7} \cdot 2 \cdot 600 \cdot 2.78}}

\frac{1}{e ^{2 \cdot 2.78 \cdot 1 0^{- 7} \cdot 600}} = \frac{1}{e ^{\frac{417}{1250000}}}

= 1 0^{3} \cdot 32.1 \cdot \frac{1}{e ^{\frac{417}{1250000}}}

Multiply fractions:

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

= 32.1 \cdot \frac{1 0 ^{3} \cdot 1}{e ^{\frac{417}{1250000}}}

\frac{1 \cdot 1 0 ^{3}}{e ^{\frac{417}{1250000}}} = \frac{1000}{e ^{\frac{417}{1250000}}}

= 32.1 \cdot \frac{1000}{e ^{\frac{417}{1250000}}}

Multiply fractions:

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

= \frac{1000 \cdot 32.1}{e ^{\frac{417}{1250000}}}

Multiply the numbers:

1000 \cdot 32.1 = 32100

= \frac{32100}{e ^{\frac{417}{1250000}}}

Convert element to a decimal form

e^{\frac{417}{1250000}} = 1.00033 \dots

= \frac{32100}{1.00033 \dots}

Divide the numbers:

\frac{32100}{1.00033 \dots} = 32089.29322 \dots

= 32089.29322 \dots

2 π \cdot 60 \cdot (1.3905 \cdot 1 0^{- 6})

2.7 \cdot 1 0^{- 4} \cdot (1 + 0.004 \cdot (0 - 20))

(e^{x - 4})^{2}

2 π x (7 x (x - 2)^{2})

e^{- k^{2}}

What is (32.1*10^3)e^{-2*(2.78*10^{-7})*600} ?
The solution to (32.1*10^3)e^{-2*(2.78*10^{-7})*600} is 32089.29322…