What is 5(10^{-5})(e^{-(284000)/(8.31(1373))}) ?

The solution to 5(10^{-5})(e^{-(284000)/(8.31(1373))}) is 7.74169E-16

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simplify 5(10^{-5})(e^{-(284000)/(8.31(1373))})

simplify

5 (1 0^{- 5}) (e^{- \frac{284000}{8.31 ( 1373 )}})

7.74169 E - 16

Solution steps

5 (1 0^{- 5}) (e^{- \frac{284000}{8.31 ( 1373 )}})

Apply exponent rule:

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

= 5 e^{- \frac{284000}{1373 \cdot 8.31}} \frac{1}{1 0 ^{5}}

Apply exponent rule:

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

= 5 \cdot \frac{1}{1 0 ^{5}} \cdot \frac{1}{e ^{\frac{284000}{1373 \cdot 8.31}}}

Multiply the numbers:

8.31 \cdot 1373 = 11409.63

= 5 \cdot \frac{1}{1 0 ^{5}} \cdot \frac{1}{e ^{\frac{284000}{11409.63}}}

Multiply fractions:

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

= \frac{1 \cdot 1 \cdot 5}{1 0 ^{5} e ^{\frac{284000}{11409.63}}}

Multiply the numbers:

1 \cdot 1 \cdot 5 = 5

= \frac{5}{1 0 ^{5} e ^{\frac{284000}{11409.63}}}

Factor

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

= \frac{5}{2 ^{5} \cdot 5 ^{5} e ^{\frac{284000}{11409.63}}}

Cancel the common factor:

5

= \frac{1}{2 ^{5} \cdot 5 ^{4} e ^{\frac{284000}{11409.63}}}

2^{5} \cdot 5^{4} e^{\frac{284000}{11409.63}} = 20000 e^{\frac{284000}{11409.63}}

= \frac{1}{20000 e ^{\frac{284000}{11409.63}}}

e^{\frac{284000}{11409.63}} = 64585395242.27673

= \frac{1}{20000 \cdot 64585395242.27673}

Multiply the numbers:

20000 \cdot 64585395242.27673 = 1.29171 E 15

= \frac{1}{1.29171 E 15}

Divide the numbers:

\frac{1}{1.29171 E 15} = 7.74169 E - 16

= 7.74169 E - 16

e^{3 x} \cdot 2 e^{x}

(x - 4)^{2} \cdot (x - 5)^{2}

\frac{1}{2 π ^{2}} \cdot e^{- \frac{1}{2} (\frac{22 - 20}{2})^{2}}

e^{- \frac{0.76}{8.02 \cdot 1 0 ^{- 5} \cdot 7.73}}

16.6 \cdot 1 0^{- 3}

What is 5(10^{-5})(e^{-(284000)/(8.31(1373))}) ?
The solution to 5(10^{-5})(e^{-(284000)/(8.31(1373))}) is 7.74169E-16