Problem Solving

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

The OA is the option C.

How can I verify which options are true? Experts, can you help me here? Please.

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.