What is 4e^{2x}x(e^{-x})(2e^{2x}) ?

The solution to 4e^{2x}x(e^{-x})(2e^{2x}) is 8e^{3x}x

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simplify 4e^{2x}x(e^{-x})(2e^{2x})

simplify

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

8 e^{3 x} x

Solution steps

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

Apply exponent rule:

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

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

= 4 x \cdot 2 e^{2 x - x + 2 x}

Add similar elements:

2 x - x + 2 x = 3 x

= 4 x \cdot 2 e^{3 x}

Multiply the numbers:

4 \cdot 2 = 8

= 8 e^{3 x} x

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What is 4e^{2x}x(e^{-x})(2e^{2x}) ?
The solution to 4e^{2x}x(e^{-x})(2e^{2x}) is 8e^{3x}x