What is e^{-5}*(5^7)/(7!)*0.1 ?

The solution to e^{-5}*(5^7)/(7!)*0.1 is 0.01044…

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simplify e^{-5}(5^7)/(7!)0.1

simplify

e^{- 5} \cdot \frac{5 ^{7}}{7 !} \cdot 0.1

0.01044 \dots

Solution steps

e^{- 5} \frac{5 ^{7}}{7 !} \cdot 0.1

Apply exponent rule:

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

= 0.1 \cdot \frac{1}{e ^{5}} \cdot \frac{5 ^{7}}{7 !}

Multiply fractions:

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

= 0.1 \cdot \frac{5 ^{7} \cdot 1}{e ^{5} \cdot 7 !}

\frac{1 \cdot 5 ^{7}}{e ^{5} \cdot 7 !} = \frac{15625}{1008 e ^{5}}

= 0.1 \cdot \frac{15625}{1008 e ^{5}}

Multiply fractions:

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

= \frac{15625 \cdot 0.1}{1008 e ^{5}}

Multiply the numbers:

15625 \cdot 0.1 = 1562.5

= \frac{1562.5}{1008 e ^{5}}

Convert element to a decimal form

e^{5} = 148.41315 \dots

= \frac{1562.5}{1008 \cdot 148.41315 \dots}

Multiply the numbers:

1008 \cdot 148.41315 \dots = 149600.46437 \dots

= \frac{1562.5}{149600.46437 \dots}

Divide the numbers:

\frac{1562.5}{149600.46437 \dots} = 0.01044 \dots

= 0.01044 \dots

\frac{1}{( 2 π 4.32 )} e^{(- \frac{1}{2} (6.60833))}

e^{- 0.0785}

1 e^{- x}

- e^{x} \cdot e^{x}

What is e^{-5}*(5^7)/(7!)*0.1 ?
The solution to e^{-5}*(5^7)/(7!)*0.1 is 0.01044…