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

The solution to e^{2x}((x^2)/2 e^{2x}) is (e^{4x}x^2)/2

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

simplify

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

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

Solution steps

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{2 x} e^{2 x} = e^{2 x + 2 x}

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

Add similar elements:

2 x + 2 x = 4 x

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

Multiply fractions:

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

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

(e^{- 2 x^{2}}) d x

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

7.65 \cdot 1 0^{- 7}

(5 x^{2} y^{3}) (3 x^{2} y^{5})

5 \cdot e^{- 25}

What is e^{2x}((x^2)/2 e^{2x}) ?
The solution to e^{2x}((x^2)/2 e^{2x}) is (e^{4x}x^2)/2