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-101^102
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20 Oct 2017, 02:42
20 Oct 2017, 02:42
Expert Reply
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Question Stats:
98% (00:12) correct
1% (00:54) wrong based on 151 sessions
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Quantity A |
Quantity B |
\((-101)^{102}\) |
\((-102)^{101}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: -101^102
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20 Oct 2017, 04:58
20 Oct 2017, 04:58
2
Without computations, quantity A is elevated to an even exponent, thus the result is positive. Quantity B, instead, is elevated to an odd exponent, thus the result is still negative.
Quantity A is greater!
Quantity A is greater!
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Joined: 10 Apr 2015
Posts: 6218
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Re: -101^102
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22 Apr 2019, 17:52
22 Apr 2019, 17:52
Carcass wrote:
Quantity A |
Quantity B |
\((-101)^{102}\) |
\((-102)^{101}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Rule #1: ODD exponents preserve the sign of the base.
So, (NEGATIVE)^(ODD integer) = NEGATIVE
and (POSITIVE)^(ODD integer) = POSITIVE
Rule #1: An EVEN exponent always yields a positive result (unless the base = 0)
So, (NEGATIVE)^(EVEN integer) = POSITIVE
and (POSITIVE)^(EVEN integer) = POSITIVE
By rule #1, Quantity A is POSITIVE
By rule #2, Quantity B is NEGATIVE
Answer: A
Cheers,
Brent
