# solving exponents

• Jan 23rd 2009, 08:53 AM
Casas4
solving exponents
I have been working on this problem for a week now and I cant solve it and Im sure its easy.
The expression e^(x-8)/e^(x-2) can be written as e^f(x), where f(x) is a function of x. Find f(x).
I tried using laws of exponents and converting it to e^(x-8)*e^(-x+2) to get e^(-6) which is still wrong. Thanks to anyone who can help.
AC
• Jan 23rd 2009, 09:12 AM
Mush
Quote:

Originally Posted by Casas4
I have been working on this problem for a week now and I cant solve it and Im sure its easy.
The expression e^(x-8)/e^(x-2) can be written as e^f(x), where f(x) is a function of x. Find f(x).
I tried using laws of exponents and converting it to e^(x-8)*e^(-x+2) to get e^(-6) which is still wrong. Thanks to anyone who can help.
AC

$\frac{e^{(x-8)}}{e^{(x-2)}} = e^{(x-8)}\times (e^{(x-2)})^{-1}$

$= e^{(x-8)}\times e^{(2-x)}$

$= e^{(x-8) + (2-x)}$

$= e^{x-8 + 2-x}$

$= e^{-6}$

You are correct.