What is 4e^{-4t}((e^{4t}-1)/4) ?

The solution to 4e^{-4t}((e^{4t}-1)/4) is (e^{4t}-1)/(e^{4t)}

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simplify 4e^{-4t}((e^{4t}-1)/4)

simplify

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

\frac{e ^{4 t} - 1}{e ^{4 t}}

Solution steps

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

Apply exponent rule:

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

= 4 \cdot \frac{1}{e ^{4 t}} \cdot \frac{e ^{4 t} - 1}{4}

Multiply fractions:

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

= \frac{1 \cdot ( e ^{4 t} - 1 ) \cdot 4}{e ^{4 t} \cdot 4}

Cancel the common factor:

4

= \frac{1 \cdot ( e ^{4 t} - 1 )}{e ^{4 t}}

1 \cdot (e^{4 t} - 1) = e^{4 t} - 1

= \frac{e ^{4 t} - 1}{e ^{4 t}}

8.9737 \times e^{- 1.96 \times 0.4975}

e^{- 3 x} \times 3 e^{3 x}

\frac{1}{21} e^{21 x} e^{- 4 x}

(8 e^{6} f^{- 4})^{- 1}

x + 4 \cdot x - 5

What is 4e^{-4t}((e^{4t}-1)/4) ?
The solution to 4e^{-4t}((e^{4t}-1)/4) is (e^{4t}-1)/(e^{4t)}