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Can $y=\frac{e^\frac{t^4}{12}}{e^{\frac{t^3}{3}}}$ be simplified?

So, I'm working on a problem and I encounter this problem instead. For some reason, the way it looks is intimidating. So this is how I'm tackling it:

I multiply the bottom denominator by 4 and obtain:

$$y=\frac{e^\frac{t^4}{12}}{e^{\frac{4t^3}{12}}}$$

so i'm wondering can I divide even though the exponents are different? If I can, then I would just get:

$$y=4e^t$$

but i'm not sure.

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  • 4
    $\begingroup$ $\frac{m^a}{m^b}=m^{a-b}$ $\endgroup$ – randomgirl Mar 27 '15 at 1:26
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    $\begingroup$ OH YEAH! !!!!!!!!!! $\endgroup$ – Justin Mar 27 '15 at 1:26
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Yes, recall that $\dfrac{e^a}{e^b} = e^{a-b}$.

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    $\begingroup$ A neat answer. +1! $\endgroup$ – Olivier Oloa Aug 27 '15 at 8:39
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$$\frac{e^{\frac{t^4}{12}}}{e^{\frac{t^3}{3}}}=e^{\frac{t^4}{12}-\frac{t^3}{3}}=...$$

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  • 2
    $\begingroup$ may be the downvoters could explain ;-) $\endgroup$ – Surb Mar 27 '15 at 1:32
  • $\begingroup$ i thought that was right o.o $\endgroup$ – Justin Mar 27 '15 at 1:37
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    $\begingroup$ What a roller-coaster! And @CSil, there's nothing wrong with this answer. You are still left to calculate the difference in the exponent, but now you know the property at work. $\endgroup$ – The Chaz 2.0 Mar 27 '15 at 1:44

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