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How does $e^{2.5-.5t}$ = $e^{2.5}$($e^{-.5t}$)

I thought that $e^{2.5-.5t}$ = $e^{2.5/.5t}$.

does the variable t make my algebra incorrect?

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    $\begingroup$ The variable $t$ shouldn't disappear. Remember that $$x^a x^b = x^{a+b}.$$ $\endgroup$ Commented Nov 20, 2014 at 1:37
  • $\begingroup$ spelling mistake $\endgroup$
    – user159778
    Commented Nov 20, 2014 at 1:39
  • $\begingroup$ Note that $a^{-b}=\dfrac1{a^b}$... $\endgroup$
    – abiessu
    Commented Nov 20, 2014 at 1:40

2 Answers 2

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when taking the product of exponents, the answer is the sum of the exponents

for example $x^a \times x^b = x^{a+b}$

but $(x^a)^b = x^{ab}$

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In general $e^{a+b} = (e^a)(e^b)$, in your case a = 2.5 and b = -0.5t

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    $\begingroup$ b=-.5t it says. $\endgroup$ Commented Nov 20, 2014 at 1:38
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    $\begingroup$ Yes, thank you. $\endgroup$
    – Piri
    Commented Nov 20, 2014 at 1:42

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