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

The solution to (4^3)/(3!)e^{-4} is (32)/(3e^4)

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

simplify

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

\frac{32}{3 e ^{4}}

Decimal Notation

0.19536 \dots

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

Multiply:

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

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

4^{3} = 64

= \frac{64}{e ^{4} \cdot 3 !}

3! e^{4} = 6 e^{4}

= \frac{64}{6 e ^{4}}

Cancel the common factor:

2

= \frac{32}{3 e ^{4}}

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