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# If a and b are negative integers, which of the following statements mu

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Math Expert
Joined: 02 Sep 2009
Posts: 51280
If a and b are negative integers, which of the following statements mu  [#permalink]

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23 Mar 2016, 10:32
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:09) correct 24% (01:19) wrong based on 151 sessions

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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

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Re: If a and b are negative integers, which of the following statements mu  [#permalink]

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23 Mar 2016, 19:32
1
Let's a = -2 and b = -3

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

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Re: If a and b are negative integers, which of the following statements mu  [#permalink]

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26 Feb 2018, 10:23
Bunuel 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.

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Re: If a and b are negative integers, which of the following statements mu &nbs [#permalink] 26 Feb 2018, 10:23
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