What is e^{-nkt}(e^{kt}-1)^{n-m} ?

The solution to e^{-nkt}(e^{kt}-1)^{n-m} is ((e^{kt}-1)^{-m+n})/(e^{nkt)}

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simplify e^{-nkt}(e^{kt}-1)^{n-m}

simplify

e^{- nk t} (e^{k t} - 1)^{n - m}

\frac{( e ^{k t} - 1 ) ^{- m + n}}{e ^{nk t}}

Solution steps

e^{- nk t} (e^{k t} - 1)^{n - m}

Apply exponent rule:

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

= \frac{1}{e ^{nk t}} (e^{k t} - 1)^{- m + n}

Multiply fractions:

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

= \frac{1 \cdot ( e ^{k t} - 1 ) ^{n - m}}{e ^{nk t}}

Multiply:

1 \cdot (e^{k t} - 1)^{n - m} = (e^{k t} - 1)^{n - m}

= \frac{( e ^{k t} - 1 ) ^{n - m}}{e ^{nk t}}

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

- 2 r e^{r^{2}} sin (θ) \cdot 2 r \cdot (- 2) sin (θ) \cdot e^{r^{2}}

4 (m^{3} n)^{5}

What is e^{-nkt}(e^{kt}-1)^{n-m} ?
The solution to e^{-nkt}(e^{kt}-1)^{n-m} is ((e^{kt}-1)^{-m+n})/(e^{nkt)}