# Math Help - Proof Question

1. ## 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

2. 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.

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

$\frac{e^a}{e^b} = e^{a-b}$

3. I am still having problems, can someone help me on this?

4. \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}