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

Question

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.

$\frac{m^a}{m^b}=m^{a-b}$ – randomgirl Mar 27 '15 at 01:26 — randomgirl, Mar 27 '15 at 01:26

score 9 · Accepted Answer · answered Mar 27 '15 at 01:26

9

Yes, recall that $\dfrac{e^a}{e^b} = e^{a-b}$.

answered Mar 27 '15 at 01:26

MathMajor

score 7 · Answer 2 · answered Mar 27 '15 at 01:26

7

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

answered Mar 27 '15 at 01:26

Surb

2

may be the downvoters could explain ;-) – Surb Mar 27 '15 at 01:32
i thought that was right o.o – Justin Mar 27 '15 at 01:37
4

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. – The Chaz 2.0 Mar 27 '15 at 01:44

2 Answers2