What is (6^4)/(4!)e^{-6} ?

The solution to (6^4)/(4!)e^{-6} is (54)/(e^6)

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simplify (6^4)/(4!)e^{-6}

simplify

\frac{6 ^{4}}{4 !} e^{- 6}

\frac{54}{e ^{6}}

Decimal Notation

0.13385 \dots

Solution steps

\frac{6 ^{4}}{4 !} e^{- 6}

Apply exponent rule:

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

= \frac{1}{e ^{6}} \cdot \frac{6 ^{4}}{4 !}

Multiply fractions:

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

= \frac{6 ^{4} \cdot 1}{4 ! e ^{6}}

Multiply:

6^{4} \cdot 1 = 6^{4}

= \frac{6 ^{4}}{e ^{6} \cdot 4 !}

6^{4} = 1296

= \frac{1296}{e ^{6} \cdot 4 !}

4! e^{6} = 24 e^{6}

= \frac{1296}{24 e ^{6}}

Divide the numbers:

\frac{1296}{24} = 54

= \frac{54}{e ^{6}}

(1.8733317 \cdot 1 0^{3}) (4.5988 \cdot 1 0^{- 48})

1.3 \cdot 1 0^{- 7}

(3.3309 \cdot 1 0^{- 25}) \cdot (1.380649 \cdot 1 0^{- 23})

(1 \cdot 1 0^{8}) (e^{- 0.157 (3)})