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Which is greater 3a^5 or (3a)^5
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25 Jan 2020, 07:02
25 Jan 2020, 07:02
1
Expert Reply
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Question Stats:
48% (00:27) correct
51% (00:18) wrong based on 52 sessions
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Quantity A |
Quantity B |
\(3a^5\) |
\((3a)^5\) |
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.
Kudos for the right answer and explanation
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Re: Which is greater 3a^5 or (3a)^5
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25 Jan 2020, 08:08
25 Jan 2020, 08:08
1
Carcass wrote:
Quantity A |
Quantity B |
\(3a^5\) |
\((3a)^5\) |
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.
Kudos for the right answer and explanation
If a is 0, Quantity A = 0 == Quantity B = 0
If a is 1, Quantity A = 3 < Quantity B = 243
Multiple answers, so the answer should be D.
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Re: Which is greater 3a^5 or (3a)^5
[#permalink]
26 Jan 2020, 07:29
26 Jan 2020, 07:29
1
Carcass wrote:
Quantity A |
Quantity B |
\(3a^5\) |
\((3a)^5\) |
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.
Kudos for the right answer and explanation
We need to compare \(3 * a^5\) and \((3a)^5 = 243 * a^5\)
Since the exponent of \(a\) is negative, we can have the following scenarios:
Scenario 1: If \(a < 0 => a^5 < 0\):
\(243 * a^5\) is a larger negative than \(3 * a^5\)
Thus: \(3 * a^5 > (3a)^5 = 243 * a^5\)
Scenario 2: If \(a = 0\):
\(3 * a^5 = (3a)^5 = 0\)
Scenario 3: If \(a > 0 => a^5 > 0\):
\(243 * a^5\) is a larger positive than \(3 * a^5\)
Thus: \(3 * a^5 < (3a)^5 = 243 * a^5\)
Thus, there is no relation between the two quantities
Answer D
