What is 12e^{-2t}*(3e^{2t}+6te^{2t}) ?

The solution to 12e^{-2t}*(3e^{2t}+6te^{2t}) is 36(2t+1)

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simplify 12e^{-2t}*(3e^{2t}+6te^{2t})

simplify

12 e^{- 2 t} \cdot (3 e^{2 t} + 6 t e^{2 t})

36 (2 t + 1)

Solution steps

12 e^{- 2 t} (3 e^{2 t} + 6 t e^{2 t})

Apply exponent rule:

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

= 12 \cdot \frac{1}{e ^{2 t}} (6 e^{2 t} t + 3 e^{2 t})

Multiply fractions:

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

= \frac{1 \cdot 12 ( 3 e ^{2 t} + 6 t e ^{2 t} )}{e ^{2 t}}

Multiply the numbers:

1 \cdot 12 = 12

= \frac{12 ( 6 e ^{2 t} t + 3 e ^{2 t} )}{e ^{2 t}}

Factor

12 (3 e^{2 t} + 6 t e^{2 t}) : 36 e^{2 t} (1 + 2 t)

= \frac{36 e ^{2 t} ( 1 + 2 t )}{e ^{2 t}}

Cancel the common factor:

e^{2 t}

= 36 (2 t + 1)

e^{- 2 t} u (- t)

3.25 x 1 0^{- 1}

- 0.6 x^{7} y^{7} \cdot (0.5 x y^{2})^{2}

e^{- \frac{3}{4} l n (x)} \cdot e^{- x}

(\frac{4 t}{( t ^{- 4} ) ^{0}})^{- 3}

What is 12e^{-2t}*(3e^{2t}+6te^{2t}) ?
The solution to 12e^{-2t}*(3e^{2t}+6te^{2t}) is 36(2t+1)