What is ((x^3+3x+1)e^{-x})e^x ?

The solution to ((x^3+3x+1)e^{-x})e^x is x^3+3x+1

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simplify ((x^3+3x+1)e^{-x})e^x

simplify

((x^{3} + 3 x + 1) e^{- x}) e^{x}

x^{3} + 3 x + 1

Solution steps

((x^{3} + 3 x + 1) e^{- x}) e^{x}

Apply exponent rule:

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

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

= (x^{3} + 3 x + 1) e^{- x + x}

Add similar elements:

- x + x = 0

= (x^{3} + 3 x + 1) e^{0}

Apply rule

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

e^{0} = 1

= 1 \cdot (x^{3} + 3 x + 1)

Multiply:

(x^{3} + 3 x + 1) \cdot 1 = (x^{3} + 3 x + 1)

= (x^{3} + 3 x + 1)

Remove parentheses:

(a) = a

= x^{3} + 3 x + 1

4000 e^{- 0.0512 (6)}

9.56 \cdot 1 0^{- 1}

42 \cdot 1 0^{- 6} \cdot 2.5

2^{3} \cdot 3^{2}

(5 c d e)^{3}

What is ((x^3+3x+1)e^{-x})e^x ?
The solution to ((x^3+3x+1)e^{-x})e^x is x^3+3x+1