Simplifying Exponential Fractions??? Easy 10!?

Question

Help me out and you'll get 10 points in under 30 minutes.

I have 32^(3/5)

I have to simplify.

The answer is 8, I know that. How do I do it without a calculator...why is it 8?

Answer 1

You probably already know that 32 = 2^5

So then:

32^(3/5) = (2^5)^(3/5)

(2^5)^(3/5) is the same thing as 2^[5*(3/5)]

Then now examine what you have so far:

2^[5*(3/5)]

Can you see that in the 5*(3/5) the 5's will cancel out?

So that leaves 2^3 = 8