# Index Laws

• November 22nd 2008, 05:47 PM
listeningintently
Index Laws
Hello :D

Here's the problem I need a hand with, I need to simplify it:

(3^2n + 5x3^n + 6)/(3^n + 3)

Thanks in advance, all help is really appreciated :)
• November 22nd 2008, 05:51 PM
o_O
Recall that: $a^{bc} = \left(a^b\right)^c$

$\frac{3^{2n} + 5\cdot 3^n + 6}{3^n + 3} = \frac{\left({\color{blue}3^n}\right)^2 + 5\cdot {\color{blue}3^n} + 6}{{\color{blue}3^n} + 6}$

Now it might be hard to see but the numerator essentially resembles a quadratic that you can factor. To see, let $\color{blue} x = 3^n$.

This yields: $\frac{{\color{blue}n}^2 + 5{\color{blue}n} + 6}{{\color{blue}n} + 6}$

Can you do it now?