Will someone please explain how this works to me? I'm going to post the actual question as a comment, need to enter it in equation form. Deals with fractional exponents and the like.

Question

anonymous · Answer

$$256^{3/4}$$ becomes $$\sqrt[4]{16,777,216}$$ I need to know how to find the answer. My calculator has a button to figure it out, but that feels like cheating. =)

mertsj · Answer

Find the 4th root of 256 first and then do the power.  Keeps the numbers smaller.

mertsj · Answer

In other words think of it like this:
$$256^{\frac{3}{4}}=(256^{\frac{1}{4}})^3$$

anonymous · Answer

Okay, but how do I do it? 

My book isn't very good at explaining things...it just kinda gives an equation with letters and then replaces it with familiar numbers, and expects ya to know how to manage the big ones. Most annoying!

mertsj · Answer

Find a number, by trial and error, that if you raise it to the 4th power you get 256.

mertsj · Answer

It can't be a very big number because 10^4 is 10000 and that is way too big.

anonymous · Answer

It's four?

mertsj · Answer

yes.  Now you know the 4th root of 256 is 4 so you can finish the problem which says to raise that to the third power.

anonymous · Answer

Okay! That makes much more sense! Thanks!

mertsj · Answer

yw