What is (2x^2+2e^{3x}+3)e^{-2x} ?

The solution to (2x^2+2e^{3x}+3)e^{-2x} is (2x^2+2e^{3x}+3)/(e^{2x)}

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simplify (2x^2+2e^{3x}+3)e^{-2x}

simplify

(2 x^{2} + 2 e^{3 x} + 3) e^{- 2 x}

\frac{2 x ^{2} + 2 e ^{3 x} + 3}{e ^{2 x}}

Solution steps

(2 x^{2} + 2 e^{3 x} + 3) e^{- 2 x}

Apply exponent rule:

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

= \frac{1}{e ^{2 x}} (2 x^{2} + 2 e^{3 x} + 3)

Multiply fractions:

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

= \frac{1 \cdot ( 2 x ^{2} + 2 e ^{3 x} + 3 )}{e ^{2 x}}

1 \cdot (2 x^{2} + 2 e^{3 x} + 3) = 2 x^{2} + 2 e^{3 x} + 3

= \frac{2 x ^{2} + 2 e ^{3 x} + 3}{e ^{2 x}}

(3.4 \cdot 1 0^{4}) \cdot (4.2 \cdot 1 0^{2})

1.0625 \cdot 2^{- 3}

k e^{- 0.8 (1)}

- 38 n^{8} \cdot r^{27} \cdot w^{3} \cdot y^{8}

0.316 \cdot 120 0^{- 0.25}

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