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((2^4)^6)^8
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20 May 2020, 08:57
20 May 2020, 08:57
Expert Reply
00:00
Question Stats:
88% (00:39) correct
11% (00:45) wrong based on 106 sessions
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Quantity A |
Quantity B |
\(((2^{4})^{6})^{8}\) |
\(((8^6)^4)^2\) |
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.
Re: ((2^4)^6)^8
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20 May 2020, 08:57
20 May 2020, 08:57
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
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((2^4)^6)^8
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21 May 2020, 05:26
21 May 2020, 05:26
1
Carcass wrote:
Quantity A |
Quantity B |
\(((2^{4})^{6})^{8}\) |
\(((8^6)^4)^2\) |
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.
Key property: \((x^a)^b = x^{ab}\)
Extension of key property: \(((x^a)^b)^c = x^{abc}\)
Apply the properties to get:
QUANTITY A: \(((2^{4})^{6})^{8}=2^{192}\)
QUANTITY B: \(((8^6)^4)^2=8^{48}\)
In order to compare these values we need the same base.
Rewrite \(8\) as \(2^3\) to get:
QUANTITY A: \(2^{192}\)
QUANTITY B: \((2^3)^{48}\)
Simplify:
QUANTITY A: \(2^{192}\)
QUANTITY B: \(2^{144}\)
Answer: A
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