What is (6^5)/(5!)*e^{-6} ?

The solution to (6^5)/(5!)*e^{-6} is (324)/(5e^6)

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simplify (6^5)/(5!)*e^{-6}

simplify

\frac{6 ^{5}}{5 !} \cdot e^{- 6}

\frac{324}{5 e ^{6}}

Decimal Notation

0.16062 \dots

Solution steps

\frac{6 ^{5}}{5 !} e^{- 6}

Apply exponent rule:

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

= \frac{1}{e ^{6}} \cdot \frac{6 ^{5}}{5 !}

Multiply fractions:

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

= \frac{6 ^{5} \cdot 1}{5 ! e ^{6}}

Multiply:

6^{5} \cdot 1 = 6^{5}

= \frac{6 ^{5}}{e ^{6} \cdot 5 !}

6^{5} = 7776

= \frac{7776}{e ^{6} \cdot 5 !}

5! e^{6} = 120 e^{6}

= \frac{7776}{120 e ^{6}}

Cancel the common factor:

24

= \frac{324}{5 e ^{6}}

\frac{1}{2} (13.509 \cdot 1 0^{- 6}) (6)^{2}

(2 \cdot 1 0^{8}) \cdot (5.5 \cdot 1 0^{- 3}) \cdot (1.1 \cdot 1 0^{- 4}) \cdot 92

e^{x} \cdot e^{e^{x}}