There's a slight problem with answer choice D.
If we let w = 0 (a non-positive integer), then w^0 = 0^0 and 0^0 is not defined (see page 141 of the Official Guide to the GRE - 3rd edition)
If 0^0 is not defined, we cannot say that 0^0 is positive.

So, there's only answer correct answer: E

Cheers,
Brent
_________________

Explanation

Remember to Plug In multiple times for must be questions. First, use an easy number, such as −1, and try it in each choice. All of the answers are positive, so don’t eliminate anything. Can we eliminate anything by making w smaller? A number such as −10 will allow us to eliminate choice (B), but everything else is still positive. But can w = 0? Non-positive just means the number can’t be positive—it doesn’t mean it can’t be zero.

	w = -1	w = 0
3w	3	0
2w+10	8	10
w^4	1	0
w^0	1	1
-w+0.5	1.5	0.5

Hence options D and E are correct.

Note: Option B is negative if w is large enough.
_________________

why not A and C ? Please elucidate.

A and C both are not positive when w=0.
_________________

Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
_________________

Is this GRE specific and does this still apply? Because 0^0 yields 1 on calculators.

From the Official Guide to the GRE General Test:


Cheers,
Brent
_________________

Option D works well, but 0 raised to 0 is not defined, and 0 is non positive number as it is non positive and non negative. This leaves us with only option E

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.