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If a and b are nonzero integers, which of the following must be negati
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19 Jan 2021, 09:46
19 Jan 2021, 09:46
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40% (02:07) wrong based on 80 sessions
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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
Kudos for the right answer and explanation
A. \((-a)^{-2b}\)
B. \((-a)^{-3b}\)
C. \(-(a^{-2b})\)
D. \(-(a^{-3b})\)
E. None of these
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
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Re: If a and b are nonzero integers, which of the following must be negati
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19 Jan 2021, 10:34
19 Jan 2021, 10:34
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Carcass wrote:
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
Kudos for the right answer and explanation
A. \((-a)^{-2b}\)
B. \((-a)^{-3b}\)
C. \(-(a^{-2b})\)
D. \(-(a^{-3b})\)
E. None of these
Kudos for the right answer and explanation
IMPORTANT CONCEPT
Rule #1: EVEN powers are always greater than or equal to zero.
So, (POSITIVE value)^(EVEN integer) > 0, and (NEGATIVE value)^(EVEN integer) > 0
So, the correct answer here is C. Here's why:
C) –[a^(-2b)]
Since b is an integer, we know that -2b is an EVEN integer.
So, we get: –[a^(EVEN integer)]
By our rule, a^(EVEN integer) is greater than or equal to zero
Since a is a NON-zero integer, we can conclude that a^(EVEN integer) is GREATER THAN zero
In other words, a^(EVEN integer) is POSITIVE
This means that -[a^(EVEN integer)] is NEGATIVE
Answer: C
Cheers,
Brent
General Discussion
Re: If a and b are nonzero integers, which of the following must be negati
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29 Apr 2022, 16:02
29 Apr 2022, 16:02
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Carcass wrote:
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
Kudos for the right answer and explanation
A. \((-a)^{-2b}\)
B. \((-a)^{-3b}\)
C. \(-(a^{-2b})\)
D. \(-(a^{-3b})\)
E. None of these
Kudos for the right answer and explanation
any number with even power - Result is positive.
Here in C - The result is positive, No matter what a is.
Then it is multiplied by -1. Hence C, Must be Negative.
