What is e^{-3}((3^0)/(0!)+(3^1)/(1!)+(3^2)/(2!)) ?

The solution to e^{-3}((3^0)/(0!)+(3^1)/(1!)+(3^2)/(2!)) is (17)/(2e^3)

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simplify e^{-3}((3^0)/(0!)+(3^1)/(1!)+(3^2)/(2!))

simplify

e^{- 3} (\frac{3 ^{0}}{0 !} + \frac{3 ^{1}}{1 !} + \frac{3 ^{2}}{2 !})

\frac{17}{2 e ^{3}}

Decimal Notation

0.42319 \dots

Solution steps

e^{- 3} (\frac{3 ^{0}}{0 !} + \frac{3 ^{1}}{1 !} + \frac{3 ^{2}}{2 !})

Apply exponent rule:

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

= \frac{1}{e ^{3}} (\frac{3 ^{0}}{0 !} + \frac{3 ^{1}}{1 !} + \frac{3 ^{2}}{2 !})

Apply rule

a^{0} = 1, a \neq = 0

3^{0} = 1

= \frac{1}{e ^{3}} (\frac{1}{0 !} + \frac{3 ^{1}}{1 !} + \frac{3 ^{2}}{2 !})

Apply rule

a^{1} = a

3^{1} = 3

= \frac{1}{e ^{3}} (\frac{1}{0 !} + \frac{3}{1 !} + \frac{3 ^{2}}{2 !})

\frac{1}{0 !} = 1

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

Join

1 + \frac{3}{1 !} + \frac{3 ^{2}}{2 !} : \frac{15}{2} + 1

= \frac{1}{e ^{3}} (\frac{15}{2} + 1)

Multiply fractions:

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

= \frac{1 \cdot ( \frac{15}{2} + 1 )}{e ^{3}}

1 \cdot (\frac{15}{2} + 1) = \frac{15}{2} + 1

= \frac{\frac{15}{2} + 1}{e ^{3}}

Join

\frac{15}{2} + 1 : \frac{17}{2}

= \frac{\frac{17}{2}}{e ^{3}}

Apply the fraction rule:

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

= \frac{17}{2 e ^{3}}

e^{- \frac{1}{2} (\frac{1}{2})^{2} \frac{1}{2}}

x^{2} y^{2} (y^{4} - 5 x^{2})

1.72 \cdot 1 0^{- 3}

3 e^{- e (3)} (3^{2} - 16) (3^{2} + 1) (3 - 1)^{4}

\frac{\frac{16}{2}}{π \cdot ( \frac{0.013}{2} ) ^{2}} \cdot 1 0^{- 3}

What is e^{-3}((3^0)/(0!)+(3^1)/(1!)+(3^2)/(2!)) ?
The solution to e^{-3}((3^0)/(0!)+(3^1)/(1!)+(3^2)/(2!)) is (17)/(2e^3)