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Which is greater (-3)^4 or (-3)^{-3}
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16 Jul 2019, 02:08
16 Jul 2019, 02:08
2
Expert Reply
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Question Stats:
96% (00:13) correct
3% (00:29) wrong based on 78 sessions
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Quantity A |
Quantity B |
\((-3)^4\) |
\((-3)^{-3}\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Which is greater (-3)^4 or (-3)^{-3}
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16 Jul 2019, 13:18
16 Jul 2019, 13:18
1
Carcass wrote:
Quantity A |
Quantity B |
\((-3)^4\) |
\((-3)^{-3}\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Two important rules:
ODD exponents preserve the sign of the base.
So, (NEGATIVE)^(ODD integer) = NEGATIVE
and (POSITIVE)^(ODD integer) = POSITIVE
An EVEN exponent always yields a positive result (unless the base = 0)
So, (NEGATIVE)^(EVEN integer) = POSITIVE
and (POSITIVE)^(EVEN integer) = POSITIVE
--------------------------------------
Since 4 is EVEN, \((-3)^4=\) some POSITIVE number
Since -3 is ODD, \((-3)^{-3}=\) some NEGATIVE number
We get:
Quantity A: some POSITIVE number
Quantity B: some NEGATIVE number
Answer: A
Cheers,
Brent
Re: Which is greater (-3)^4 or (-3)^{-3}
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05 Mar 2023, 16:28
05 Mar 2023, 16:28
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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