What is 2/5 (e^{-5t})(t^{-1}) ?

The solution to 2/5 (e^{-5t})(t^{-1}) is 2/(5e^{5t)t}

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simplify 2/5 (e^{-5t})(t^{-1})

simplify

\frac{2}{5} (e^{- 5 t}) (t^{- 1})

\frac{2}{5 e ^{5 t} t}

Solution steps

\frac{2}{5} (e^{- 5 t}) (t^{- 1})

Apply exponent rule:

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

= \frac{2}{5} \cdot \frac{1}{e ^{5 t}} t^{- 1}

Apply exponent rule:

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

= \frac{2}{5} \cdot \frac{1}{e ^{5 t}} \cdot \frac{1}{t}

Multiply fractions:

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

= \frac{2 \cdot 1 \cdot 1}{5 e ^{5 t} t}

Multiply the numbers:

2 \cdot 1 \cdot 1 = 2

= \frac{2}{5 e ^{5 t} t}

e^{- x} \cdot (e^{x + y})

\frac{1 ^{n}}{2 ^{n}}

12 \cdot e^{- 2}

, (5^{- 12})^{\frac{1}{3}}

- 0.5 (7 + 2)^{- \frac{3}{2}}

What is 2/5 (e^{-5t})(t^{-1}) ?
The solution to 2/5 (e^{-5t})(t^{-1}) is 2/(5e^{5t)t}