What is e^{-10t}u_{3}(t-3)^3 ?

The solution to e^{-10t}u_{3}(t-3)^3 is (u_{3}(t-3)^3)/(e^{10t)}

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simplify e^{-10t}u_{3}(t-3)^3

simplify

e^{- 10 t} u_{3} (t - 3)^{3}

\frac{u _{3} ( t - 3 ) ^{3}}{e ^{10 t}}

Solution steps

e^{- 10 t} u_{3} (t - 3)^{3}

Apply exponent rule:

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

= \frac{1}{e ^{10 t}} u_{3} (t - 3)^{3}

Multiply fractions:

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

= \frac{1 \cdot u _{3} ( t - 3 ) ^{3}}{e ^{10 t}}

Multiply:

1 \cdot u_{3} = u_{3}

= \frac{u _{3} ( t - 3 ) ^{3}}{e ^{10 t}}

e^{- 2.325}

3.44 e^{- 9}

[1 - cos (α t)] e^{- βt}

(e^{5})^{x}

What is e^{-10t}u_{3}(t-3)^3 ?
The solution to e^{-10t}u_{3}(t-3)^3 is (u_{3}(t-3)^3)/(e^{10t)}