What is e^{-4}(4^5)/(5!) ?

The solution to e^{-4}(4^5)/(5!) is (128)/(15e^4)

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simplify e^{-4}(4^5)/(5!)

simplify

e^{- 4} \frac{4 ^{5}}{5 !}

\frac{128}{15 e ^{4}}

Decimal Notation

0.15629 \dots

Solution steps

e^{- 4} \frac{4 ^{5}}{5 !}

Apply exponent rule:

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

= \frac{1}{e ^{4}} \cdot \frac{4 ^{5}}{5 !}

Multiply fractions:

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

= \frac{1 \cdot 4 ^{5}}{e ^{4} \cdot 5 !}

Multiply:

1 \cdot 4^{5} = 4^{5}

= \frac{4 ^{5}}{e ^{4} \cdot 5 !}

4^{5} = 1024

= \frac{1024}{e ^{4} \cdot 5 !}

e^{4} \cdot 5! = 120 e^{4}

= \frac{1024}{120 e ^{4}}

Cancel the common factor:

8

= \frac{128}{15 e ^{4}}

e^{- 2 t} cos (5 t) e^{- s t}

1.0672 \cdot 10 \cdot (4 π \cdot 1 0^{- 7})

\frac{1}{2} (3) (33)

e^{- 2 (1.5)}

1.23 \cdot 1 0^{- 2}