What is t^{-8}e^{2t}*te^{2t} ?

The solution to t^{-8}e^{2t}*te^{2t} is (e^{4t})/(t^7)

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simplify t^{-8}e^{2t}*te^{2t}

simplify

t^{- 8} e^{2 t} \cdot t e^{2 t}

\frac{e ^{4 t}}{t ^{7}}

Solution steps

t^{- 8} e^{2 t} t e^{2 t}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{2 t} e^{2 t} = e^{2 t + 2 t}

= t^{- 8} t e^{2 t + 2 t}

Add similar elements:

2 t + 2 t = 4 t

= t^{- 8} t e^{4 t}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

t^{- 8} t = t^{- 8 + 1}

= t^{- 8 + 1} e^{4 t}

Add/Subtract the numbers:

- 8 + 1 = - 7

= t^{- 7} e^{4 t}

Apply exponent rule:

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

t^{- 7} = \frac{1}{t ^{7}}

= e^{4 t} \frac{1}{t ^{7}}

Multiply fractions:

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

= \frac{1 \cdot e ^{4 t}}{t ^{7}}

Multiply:

1 \cdot e^{4 t} = e^{4 t}

= \frac{e ^{4 t}}{t ^{7}}

(22) \cdot 3

(4 X^{3} Y^{5} Z) (6 X^{5} Y^{4} Z)

e^{t} \frac{d}{d t} ((Q (t)) Q (t) e^{t})

(4300) (1.96)^{2} (0.5) (0.5)

What is t^{-8}e^{2t}*te^{2t} ?
The solution to t^{-8}e^{2t}*te^{2t} is (e^{4t})/(t^7)