What is (-4e^{-4t}2e^{2t}4)*(e^{-4t}e^{2t}4t) ?

The solution to (-4e^{-4t}2e^{2t}4)*(e^{-4t}e^{2t}4t) is -128e^{-4t}t

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simplify (-4e^{-4t}2e^{2t}4)*(e^{-4t}e^{2t}4t)

simplify

(- 4 e^{- 4 t} 2 e^{2 t} 4) \cdot (e^{- 4 t} e^{2 t} 4 t)

- 128 e^{- 4 t} t

Solution steps

(- 4 e^{- 4 t} \cdot 2 e^{2 t} \cdot 4) (e^{- 4 t} e^{2 t} \cdot 4 t)

Apply exponent rule:

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

e^{- 4 t} e^{2 t} = e^{- 4 t + 2 t}

= (- 4 e^{- 4 t} \cdot 2 e^{2 t} \cdot 4) e^{- 4 t + 2 t} \cdot 4 t

Add similar elements:

- 4 t + 2 t = - 2 t

= (- 4 e^{- 4 t} \cdot 2 e^{2 t} \cdot 4) e^{- 2 t} \cdot 4 t

Remove parentheses:

(- a) = - a

= - 4 e^{- 4 t} \cdot 2 e^{2 t} \cdot 4 e^{- 2 t} \cdot 4 t

Multiply the numbers:

4 \cdot 2 \cdot 4 \cdot 4 = 128

= - 128 e^{- 4 t} e^{2 t} e^{- 2 t} t

Apply exponent rule:

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

e^{- 4 t} e^{2 t} e^{- 2 t} = e^{- 4 t + 2 t - 2 t}

= - 128 e^{- 4 t + 2 t - 2 t} t

Add similar elements:

- 4 t + 2 t - 2 t = - 4 t

= - 128 e^{- 4 t} t

15. 4^{2} \cdot \frac{1. 8 ^{2}}{1. 1 ^{2}}

1.38 \cdot 1 0^{- 23} \cdot 298 \cdot ln (1 0^{2.19})

- \frac{e ^{- x}}{e ^{- 2 x}}

3 + 2 \cdot 3 - 2

e^{(- 150 \cdot 720 \cdot 1 0^{- 6})}

What is (-4e^{-4t}2e^{2t}4)*(e^{-4t}e^{2t}4t) ?
The solution to (-4e^{-4t}2e^{2t}4)*(e^{-4t}e^{2t}4t) is -128e^{-4t}t