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

The solution to e^{-5}(5^6)/(6!) is (3125)/(144e^5)

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

simplify

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

\frac{3125}{144 e ^{5}}

Decimal Notation

0.14622 \dots

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

Multiply:

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

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

5^{6} = 15625

= \frac{15625}{e ^{5} \cdot 6 !}

e^{5} \cdot 6! = 720 e^{5}

= \frac{15625}{720 e ^{5}}

Cancel the common factor:

5

= \frac{3125}{144 e ^{5}}

1 \cdot 1 0^{- 3} e^{\frac{- 0.7}{0.026}}

0. 3^{- 3}

e^{x} \times e^{x^{2}}

(3)^{1 - x} \times 9^{1 - 2 x}

e^{- 4}