What is e^{-t}(8e^t+45e^{6t}) ?

The solution to e^{-t}(8e^t+45e^{6t}) is 45e^{5t}+8

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simplify e^{-t}(8e^t+45e^{6t})

simplify

e^{- t} (8 e^{t} + 45 e^{6 t})

45 e^{5 t} + 8

Solution steps

e^{- t} (8 e^{t} + 45 e^{6 t})

Apply exponent rule:

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

= \frac{1}{e ^{t}} (8 e^{t} + 45 e^{6 t})

Multiply fractions:

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

= \frac{1 \cdot ( 8 e ^{t} + 45 e ^{6 t} )}{e ^{t}}

1 \cdot (8 e^{t} + 45 e^{6 t}) = 8 e^{t} + 45 e^{6 t}

= \frac{8 e ^{t} + 45 e ^{6 t}}{e ^{t}}

Factor

8 e^{t} + 45 e^{6 t} : e^{t} (8 + 45 e^{5 t})

= \frac{e ^{t} ( 8 + 45 e ^{5 t} )}{e ^{t}}

Cancel the common factor:

e^{t}

= 8 + 45 e^{5 t}

680180180.18 \cdot 1 0^{- 6}

15 e^{- \frac{3}{5}}

(0.28 \cdot (1 0^{- 3})) (60000)

\frac{- 30}{6}

c^{5} c \frac{π}{6}

What is e^{-t}(8e^t+45e^{6t}) ?
The solution to e^{-t}(8e^t+45e^{6t}) is 45e^{5t}+8