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

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

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

simplify

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

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

Decimal Notation

0.16062 \dots

Solution steps

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

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

Multiply:

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

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

6^{5} = 7776

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

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

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

Cancel the common factor:

24

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

e^{- \frac{1}{2} l n (c o s (x))}

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

x^{2} (x - 2)^{2} (x - 1)^{2}