What is e^{-8}*(8^6)/(6!) ?

The solution to e^{-8}*(8^6)/(6!) is (16384)/(45e^8)

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simplify e^{-8}*(8^6)/(6!)

simplify

e^{- 8} \cdot \frac{8 ^{6}}{6 !}

\frac{16384}{45 e ^{8}}

Decimal Notation

0.12213 \dots

Solution steps

e^{- 8} \frac{8 ^{6}}{6 !}

Apply exponent rule:

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

= \frac{1}{e ^{8}} \cdot \frac{8 ^{6}}{6 !}

Multiply fractions:

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

= \frac{1 \cdot 8 ^{6}}{e ^{8} \cdot 6 !}

Multiply:

1 \cdot 8^{6} = 8^{6}

= \frac{8 ^{6}}{e ^{8} \cdot 6 !}

8^{6} = 262144

= \frac{262144}{e ^{8} \cdot 6 !}

e^{8} \cdot 6! = 720 e^{8}

= \frac{262144}{720 e ^{8}}

Cancel the common factor:

16

= \frac{16384}{45 e ^{8}}

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What is e^{-8}*(8^6)/(6!) ?
The solution to e^{-8}*(8^6)/(6!) is (16384)/(45e^8)