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If \(a\) and \(b\) are nonzero integers, which of the following must be negative?

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If \(a\) and \(b\) are nonzero integers, which of the following must be negative?

by M7MBA » Wed May 20, 2020 7:30 am

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If \(a\) and \(b\) are nonzero integers, which of the following must be negative?

A. \((−a)^{−2b}\)

B. \((−a)^{−3b}\)

C. \(−a^{−2b}\)

D. \(−a^{−3b}\)

E. None of these

[spoiler]OA=C[/spoiler]

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Re: If \(a\) and \(b\) are nonzero integers, which of the following must be negative?

by Scott@TargetTestPrep » Mon May 25, 2020 10:54 am
M7MBA wrote: ↑
Wed May 20, 2020 7:30 am
 If \(a\) and \(b\) are nonzero integers, which of the following must be negative?

A. \((−a)^{−2b}\)

B. \((−a)^{−3b}\)

C. \(−a^{−2b}\)

D. \(−a^{−3b}\)

E. None of these

[spoiler]OA=C[/spoiler]

Solution:

Since -2b must be even regardless of whether b is odd or even, a^(-2b) will be positive regardless of whether a is positive or negative. Therefore, -a^(-2b) must be negative.

Answer: C

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