Of course, you can always get a quick answer by trying some examples in your calculator. But that wouldn't be much fun, would it? :)
Let's consider a positive base of 2.
Clearly, 2^1 = 2
2^2 = 2 * 2 = 4
2^3 = 2 * 2 * 2 = 8
2^4 = 2 * 2 * 2 * 2 = 16
and so on. . .
Notice that everytime the exponent increases by 1, the answer gets twice as big.
Now, run things in reverse. What happens every time the exponent decreases by 1?
Clearly, we divide by 2 each time. We go from 16 -> 8 -> 4 ->2.
So, if 2^1 = 2, what would you expect 2^0 to equal?
Hopefully, you can see that we simply divide by 2 again to get from 2 to 2/2 = 1.
Continuing this pattern of dividing by 2 when the exponent decreases, we get. . .
2^-1 = 1/2
2^-2 = 1/4
2^-3 = 1/8
etc.
Notice that each time, the number gets closer to 0 each time (in fact, twice as close), but it never changes sign. Hopefully, you see that we can divide by 2 as many times as we want and we'll never change sign. We'll just get closer to 0.
If we had a different base than 2, then we would just be dividing by a different positive number each time the exponent decreased. But no matter how many times you divide by a positive number--when you start with a positive number, the result will remain positive.
So, in general, a positive number raised to a negative exponent will always be positive.
Hope this helps!