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

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

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

simplify

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

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

Decimal Notation

0.16803 \dots

Solution steps

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

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

Multiply:

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

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

3^{4} = 81

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

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

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

Cancel the common factor:

3

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

2.9 \cdot 1^{- 9999}

2 e^{- x} (e^{x})

3 x (2 x^{3} + 5)

3.42917 \cdot 1 0^{- 4}