What is e^{-3}(3^4)/(4!) ?

The solution to e^{-3}(3^4)/(4!) is (27)/(8e^3)

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simplify e^{-3}(3^4)/(4!)

simplify

e^{- 3} \frac{3 ^{4}}{4 !}

\frac{27}{8 e ^{3}}

Decimal Notation

0.16803 \dots

Solution steps

e^{- 3} \frac{3 ^{4}}{4 !}

Apply exponent rule:

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

= \frac{1}{e ^{3}} \cdot \frac{3 ^{4}}{4 !}

Multiply fractions:

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

= \frac{1 \cdot 3 ^{4}}{e ^{3} \cdot 4 !}

Multiply:

1 \cdot 3^{4} = 3^{4}

= \frac{3 ^{4}}{e ^{3} \cdot 4 !}

3^{4} = 81

= \frac{81}{e ^{3} \cdot 4 !}

e^{3} \cdot 4! = 24 e^{3}

= \frac{81}{24 e ^{3}}

Cancel the common factor:

3

= \frac{27}{8 e ^{3}}

5 e^{- 0.3}

3.3 e^{- 5}

164.98538 \cdot 1 0^{- 7}

3.3 e^{- 1}