What is e^{-3*2}*((3*2)^6)/(6!) ?

The solution to e^{-3*2}*((3*2)^6)/(6!) is (324)/(5e^6)

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simplify e^{-32}((3*2)^6)/(6!)

simplify

e^{- 3 \cdot 2} \cdot \frac{( 3 \cdot 2 ) ^{6}}{6 !}

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

Decimal Notation

0.16062 \dots

Solution steps

e^{- 3 \cdot 2} \frac{( 3 \cdot 2 ) ^{6}}{6 !}

Apply exponent rule:

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

= \frac{1}{e ^{3 \cdot 2}} \cdot \frac{( 3 \cdot 2 ) ^{6}}{6 !}

Multiply the numbers:

3 \cdot 2 = 6

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

Multiply fractions:

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

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

Multiply:

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

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

6^{6} = 46656

= \frac{46656}{e ^{6} \cdot 6 !}

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

= \frac{46656}{720 e ^{6}}

Cancel the common factor:

144

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

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What is e^{-3*2}*((3*2)^6)/(6!) ?
The solution to e^{-3*2}*((3*2)^6)/(6!) is (324)/(5e^6)