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

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

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simplify (e^t(2e^t)^2)/(e^{-t)}

simplify

\frac{e ^{t} ( 2 e ^{t} ) ^{2}}{e ^{- t}}

4 e^{4 t}

Solution steps

\frac{e ^{t} ( 2 e ^{t} ) ^{2}}{e ^{- t}}

Apply exponent rule:

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

\frac{e ^{t}}{e ^{- t}} = e^{t - (- t)} = e^{2 t}

= e^{2 t} (2 e^{t})^{2}

(2 e^{t})^{2} = 2^{2} e^{2 t}

= 2^{2} e^{2 t} e^{2 t}

Apply exponent rule:

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

e^{2 t} e^{t \cdot 2} = e^{2 t + 2 t}

= 2^{2} e^{2 t + t \cdot 2}

Add similar elements:

2 t + 2 t = 4 t

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

2^{2} = 4

= 4 e^{4 t}

5 p + 3 p + (- 9)

\frac{p ^{6}}{p ^{- 2}}

\frac{e ^{3 x} + 1}{e ^{x} + 1}

x^{3} - x^{4}

31 + 21 + 13 + 9

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