Hi- i got this problem correct and it was a lucky guess. Can someone explain the rules to this and provide an explanation?

2^5 +2 ^5 +3^5 +3^5 +3^5?

Thanks!!

Since the root is constant, you can simply add the numbers preceeding the root, keeping the root same.
2^5+2^5+3^5+3^5+3^5= 13^5

Please post the entire problem if you would like an instructor to apply. Also, Khalid, your calculation is not correct.

Try this:
2^2 + 2^2 = 4 + 4 = 8
but if I followed your calculation, I'd end up with 4^2 = 16. Not the same number.

I don't know whether it is the fastest way, but here is a solution

2^5 +2 ^5 +3^5 +3^5 +3^5 = 2*2^5 + 3*3^5 = 2*32+3*243=64+729=793
or = 2^6+3^6 = 793
It would be great to see the answer chioces.

The last post has the correct answer, but glosses over WHY it's the correct answer. Specifically,
2 * (2^5) is 2 * (2*2*2*2*2), which is 2*2*2*2*2*2 = 2^6.
The same reasoning shows that 3 * (3^5) is 3^6; try this yourself and make sure that you can derive it.

I'm assuming that the answer choices (which you didn't post) were left in exponential form: i.e., the correct answer was in all likelihood written as 2^6 + 3^6. I'd be awfully surprised if the GMAT actually wanted you to calculate the answer.

Incidentally, the numbers in this problem aren't all that big, so you could just multiply the original expression out - 32 + 32 + 243 + 243 + 243 = 793 - and then do the same with the answer choices. It's ugly, but you could probably do it in two minutes if you concentrate really hard (and if you haven't grown up using a calculator since the age of six).