What is 4e^{-2t}*(-7/16)t^2e^{1/2 t} ?

The solution to 4e^{-2t}*(-7/16)t^2e^{1/2 t} is -(7e^{-(3t)/2}t^2)/(4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 4e^{-2t}*(-7/16)t^2e^{1/2 t}

simplify

4 e^{- 2 t} \cdot (- \frac{7}{16}) t^{2} e^{\frac{1}{2} t}

- \frac{7 e ^{- \frac{3 t}{2}} t ^{2}}{4}

Solution steps

4 e^{- 2 t} (- \frac{7}{16}) t^{2} e^{\frac{1}{2} t}

Apply exponent rule:

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

e^{- 2 t} e^{\frac{1}{2} t} = e^{- 2 t + \frac{1}{2} t}

= 4 (- \frac{7}{16}) t^{2} e^{- 2 t + \frac{1}{2} t}

Remove parentheses:

(- a) = - a

= - 4 \cdot \frac{7}{16} t^{2} e^{- 2 t + \frac{1}{2} t}

Multiply fractions:

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

= - \frac{7 \cdot 4 t ^{2} e ^{- 2 t + \frac{1}{2} t}}{16}

7 \cdot 4 t^{2} e^{- 2 t + \frac{1}{2} t} = 28 e^{- \frac{3}{2} t} t^{2}

= - \frac{28 e ^{- \frac{3}{2} t} t ^{2}}{16}

Cancel the common factor:

4

= - \frac{7 e ^{- \frac{3}{2} t} t ^{2}}{4}

e^{- \frac{3}{2} t} = e^{- \frac{3 t}{2}}

= - \frac{7 e ^{- \frac{3 t}{2}} t ^{2}}{4}

e^{x} e^{3}

(\frac{1}{3})^{- 6 π}

(3.1 \cdot 1 0^{- 11}) 1 0^{\frac{36}{10}}

22.68 \cdot e^{- 0.0183} \cdot 9.9

- 100 \cdot 1 0^{3} \cdot 20 \cdot 1 0^{- 9} ln (\frac{10 - 5}{10 + 5})

What is 4e^{-2t}*(-7/16)t^2e^{1/2 t} ?
The solution to 4e^{-2t}*(-7/16)t^2e^{1/2 t} is -(7e^{-(3t)/2}t^2)/(4)