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

The solution to e^{-2}*(2^2)/(2!) is 2/(e^2)

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

simplify

e^{- 2} \cdot \frac{2 ^{2}}{2 !}

\frac{2}{e ^{2}}

Solution steps

e^{- 2} \frac{2 ^{2}}{2 !}

Apply exponent rule:

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

= \frac{1}{e ^{2}} \cdot \frac{2 ^{2}}{2 !}

Multiply fractions:

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

= \frac{1 \cdot 2 ^{2}}{e ^{2} \cdot 2 !}

Multiply:

1 \cdot 2^{2} = 2^{2}

= \frac{2 ^{2}}{e ^{2} \cdot 2 !}

2^{2} = 4

= \frac{4}{e ^{2} \cdot 2 !}

e^{2} \cdot 2! = 2 e^{2}

= \frac{4}{2 e ^{2}}

Divide the numbers:

\frac{4}{2} = 2

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

(100) (e^{x})^{9 - 1}

6 (3 \cdot 3 + 2)^{- 1} \cdot 2.4

5 e^{- 0.6 t}

3800 (1 + 0.07)^{- 5}

380.384 \cdot (70 \cdot 1 0^{- 3})