1. ## simplifying exponents

Right now in school we are covering limits but also doing a review. I have to simplify some exponents and got all of them on the assingment except two problems. They both involve exponents with different bases. The problems are

10^2x 2^10x

and

3^x + 4^x / 5^x

How would I go in approaching to solve these problems?

Also I am not sure if I simplified a problem enogh

The problem is

(1/8)^-pi/3

and I simplified it to 8^-pi/3.

Is there a way to simplify this answer further.

2. #1: $\displaystyle 10^{2x} \cdot 2^{10x}$

Use the fact that: $\displaystyle a^cb^c = (ab)^c$ (Imagine $\displaystyle c = x$)

#2: $\displaystyle \frac{3^x + 4^x}{5^x}$

Not much to do here ...

#3: $\displaystyle \left(\frac{1}{8}\right)^{-\frac{\pi}{3}} = 8^{{\color{red}+}\frac{\pi}{3}}$ (No negative sign)

Not much to do here either.

3. Originally Posted by o_O
#3: $\displaystyle \left(\frac{1}{8}\right)^{-\frac{\pi}{3}} = 8^{{\color{red}+}\frac{\pi}{3}}$ (No negative sign)

Not much to do here either.
You could go the extra step and see that $\displaystyle 8^{\frac{1}{3}}=2$, so it could be simplified to $\displaystyle 2^{\pi}$.

--Chris