What is (3^5)/(5!)(e^{-3}) ?

The solution to (3^5)/(5!)(e^{-3}) is (81)/(40e^3)

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simplify (3^5)/(5!)(e^{-3})

simplify

\frac{3 ^{5}}{5 !} (e^{- 3})

\frac{81}{40 e ^{3}}

Solution steps

\frac{3 ^{5}}{5 !} (e^{- 3})

Apply exponent rule:

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

= \frac{1}{e ^{3}} \cdot \frac{3 ^{5}}{5 !}

Multiply fractions:

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

= \frac{3 ^{5} \cdot 1}{5 ! e ^{3}}

Multiply:

3^{5} \cdot 1 = 3^{5}

= \frac{3 ^{5}}{e ^{3} \cdot 5 !}

3^{5} = 243

= \frac{243}{e ^{3} \cdot 5 !}

5! e^{3} = 120 e^{3}

= \frac{243}{120 e ^{3}}

Cancel the common factor:

3

= \frac{81}{40 e ^{3}}

6 y^{2} (2 y^{\circ})^{2}

6.62 \cdot 1 0^{- 16} \cdot 9.8049

3 - x x^{2} - 4

6 x^{2} \cdot 0. 5^{- 2}