What is x^2e^{-1/2 (x-2)^2} ?

The solution to x^2e^{-1/2 (x-2)^2} is (x^2}{e^{\frac{(x-2)^2)/2}}

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simplify x^2e^{-1/2 (x-2)^2}

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

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

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

Multiply fractions:

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

= \frac{1 \cdot x ^{2}}{e ^{\frac{( x - 2 ) ^{2}}{2}}}

Multiply:

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

= \frac{x ^{2}}{e ^{\frac{( x - 2 ) ^{2}}{2}}}

1.786 \cdot 1 0^{- 6}

ab^{\frac{1}{3}}

(5 C^{2}) (7 C^{3})

\frac{3}{8} e^{- \frac{3}{8}}

24391.7 \cdot 30. 5^{- 1.0221}

What is x^2e^{-1/2 (x-2)^2} ?
The solution to x^2e^{-1/2 (x-2)^2} is (x^2}{e^{\frac{(x-2)^2)/2}}