# Proof Question

• Dec 17th 2008, 08:33 AM
jp.101
Proof Question
Hi there,

i have been stuck on this problem all day.

I have to show that the following expression

t = exp(3x)exp(3y)exp(z+7) / exp(z+x+3y+5)exp(x+2)

can be written as t = exp(x)

i have had many solutions obviously none of which are correct, does rules of powers and indices still hold for exponential values?

Any help would be greatly appreciated

JP
• Dec 17th 2008, 08:44 AM
Chop Suey
Quote:

Originally Posted by jp.101
i have had many solutions obviously none of which are correct, does rules of powers and indices still hold for exponential values?

Yes.

$\displaystyle e^a e^b = e^{a+b}$

$\displaystyle \frac{e^a}{e^b} = e^{a-b}$
• Dec 17th 2008, 09:20 AM
jp.101
I am still having problems, can someone help me on this?
• Dec 17th 2008, 12:19 PM
o_O
\displaystyle \begin{aligned} t & = \frac{e^{3x}e^{3y}e^{z+7}} {e^{z+x+3y+5} \ e^{x+2}} \\ & = \frac{ e^{3x + 3y + z + 7}}{e^{z+2x+3y+7}} \qquad \text{Since: } e^ae^b = e^{a+b} \\ & = e^{x} \qquad \qquad \quad \ \ \text{Since: } \frac{e^a}{e^b} = e^{a-b} \end{aligned}