What is (4e^xx^3-12e^xx^2+21e^xx+x-21e^x)*e^{-x} ?

The solution to (4e^xx^3-12e^xx^2+21e^xx+x-21e^x)*e^{-x} is (4e^xx^3-12e^xx^2+21e^xx+x-21e^x)/(e^x)

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simplify (4e^xx^3-12e^xx^2+21e^xx+x-21e^x)*e^{-x}

simplify

(4 e^{x} x^{3} - 12 e^{x} x^{2} + 21 e^{x} x + x - 21 e^{x}) \cdot e^{- x}

\frac{4 e ^{x} x ^{3} - 12 e ^{x} x ^{2} + 21 e ^{x} x + x - 21 e ^{x}}{e ^{x}}

Solution steps

(4 e^{x} x^{3} - 12 e^{x} x^{2} + 21 e^{x} x + x - 21 e^{x}) e^{- x}

Apply exponent rule:

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

= \frac{1}{e ^{x}} (4 e^{x} x^{3} - 12 e^{x} x^{2} + 21 e^{x} x + x - 21 e^{x})

Multiply fractions:

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

= \frac{1 \cdot ( 4 e ^{x} x ^{3} - 12 e ^{x} x ^{2} + 21 e ^{x} x + x - 21 e ^{x} )}{e ^{x}}

1 \cdot (4 e^{x} x^{3} - 12 e^{x} x^{2} + 21 e^{x} x + x - 21 e^{x}) = 4 e^{x} x^{3} - 12 e^{x} x^{2} + 21 e^{x} x + x - 21 e^{x}

= \frac{4 e ^{x} x ^{3} - 12 e ^{x} x ^{2} + 21 e ^{x} x + x - 21 e ^{x}}{e ^{x}}

- e^{x} e^{- x}

(4.5 \cdot 1 0^{21}) (1.602 \cdot 1 0^{- 19})

2 e^{- l n (6)}

1.252 \cdot 1 0^{- 3}

4 e^{- 1.5}

What is (4e^xx^3-12e^xx^2+21e^xx+x-21e^x)*e^{-x} ?
The solution to (4e^xx^3-12e^xx^2+21e^xx+x-21e^x)*e^{-x} is (4e^xx^3-12e^xx^2+21e^xx+x-21e^x)/(e^x)