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.
If a and b are negative integers, which of the . . . .
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- EconomistGMATTutor
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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.
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.
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- Jeff@TargetTestPrep
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We can say a = -2, and b = -1.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
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
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