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

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

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}}

4444 \cdot (0.4 \cdot 1 0^{- 3})

3.623 \cdot 1 0^{- 3}

- 22 0.1

a^{2} \cdot q^{2}