If a and b are negative integers, which of the . . . .

Hello Vincen.

Let's take a look at your question.

If we choose a = -2 and b = -3, we will have

I. (-a)^b = (2)^(-3) = 1/(2^3) --> Positive
II. (-a)^(-b) = 2^3 --> Positive
III. a^(-b) = -2^3 --> Negative

Then, the correct answer is the option C.

I hope this answer can help you to understand.

I'm available if you'd like a follow-up.

Regards.

Vincen wrote:If a and b are negative integers, which of the following statements must be true?

I. (-a)^b is positive.
II. (-a)^(-b) is positive.
III. a^(-b) is positive.

A. None
B. II only
C. I and II only
D. I and III only
E. I, II and III

We can say a = -2, and b = -1.

I. (-a)^b = (-(-2))^-1 = 2^-1 = 1/2

Thus, (-a)^b is positive.

II.(-a)^(-b) = (-(-2))^(-(-1)) = 2^1 = 2

Thus, (-a)^(-b) is positive.

III. a^(-b) = -2^-(-1) = -2^1 = -2

Thus, a^(-b) IS NOT positive.

Answer: C