Since the base is negative, we know that even powers will turn the result positive and fulfill the inequality \((\frac{-1}{2})^N > -8\).

So right off, we can select Choices A and F. The exponent -10 will become +10 when we take the reciprocal of the base -1/2, which will turn into -2, and since 10 is even, the result will be positive. And the positive exponent +10 (Choice F) will yield us only a positive result.

and Choice D will yield 1 which is greater than -8

What about the odd powers?

Odd powers will preserve the negative sign of the base, and the result will be negative. But the inequality could be fulfilled if the negative number is greater than -8 - which means the absolute value of the result should be less than 8.

Choice C, with negative exponent of -3 will give us a value of -8. So we reject it, as it breaks the inequality.

Choice B, with negative exponent of -7 will give us a value less than -8, so we can reject it even without calculating the actual value.

Choice E, with positive exponent 3, will give us a value greater than -8, since -1/2 itself is greater than -8 and if it is raised to a power, its value becomes even greater than -8.

Thus the correct answer are A,D,E,F.