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Popular >

simplify (x^2xe^{2x})e^{-2x}

Solution

simplify

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

Solution

x^{3}

Solution steps

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

= x^{2} x e^{2 x - 2 x}

Add similar elements:

2 x - 2 x = 0

= x^{2} x e^{0}

Apply exponent rule:

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

x^{2} x = x^{2 + 1}

= x^{2 + 1} e^{0}

Add the numbers:

2 + 1 = 3

= x^{3} e^{0}

Apply rule

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

e^{0} = 1

= 1 \cdot x^{3}

Multiply:

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

= x^{3}

Popular Examples

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45.2 \cdot 1 0^{- 1}

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0.9906 \cdot 1 0^{- 3} \cdot 7.2666 \cdot (1000 - 7.2666)

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Frequently Asked Questions (FAQ)

What is (x^2xe^{2x})e^{-2x} ?
The solution to (x^2xe^{2x})e^{-2x} is x^3