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Popular >

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

Solution

simplify

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

Solution

e^{t}

Solution steps

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

(e^{t})^{2} : e^{t \cdot 2}

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

Apply exponent rule:

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

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

Multiply fractions:

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

= \frac{1 \cdot e ^{t \cdot 2}}{e ^{t}}

Multiply:

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

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

Apply exponent rule:

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

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

= e^{t}

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Frequently Asked Questions (FAQ)

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