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18 Jun 2024, 23:55
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
100% (01:34) correct
0% (00:00) wrong based on 1 sessions
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x and m are positive numbers, and m is a multiple of 3.
Quantity A
\(\frac{x^m}{x^3}\)
Quantity B
\(x^{\frac{m}{3}}\)
Quantity A
\(\frac{x^m}{x^3}\)
Quantity B
\(x^{\frac{m}{3}}\)
13 Jul 2024, 11:34
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Official Explanation
Since \(\frac{x^m}{x^3} = x^{m-3}\), you need to compare \(x^{m-3}\) with \(x^{\frac{m}{3}}\). Since the base in both expressions is the same, a good strategy to use to solve this problem is to plug in numbers for m in both expressions and compare them.
You know that m is a multiple of 3, so the least positive integer you can plug in for m is 3.
If \(m = 3\), then \(x^{m-3} =1\) and \(x^\frac{m}{3} =x\). Since x can be any positive number, its relationship to 1 cannot be determined from the information given. This example is sufficient to show that the relationship between \(\frac{x^m}{x^3}\) and \(x^{\frac{m}{3}}\) cannot be determined from the information given. The correct answer is Choice D.
Since \(\frac{x^m}{x^3} = x^{m-3}\), you need to compare \(x^{m-3}\) with \(x^{\frac{m}{3}}\). Since the base in both expressions is the same, a good strategy to use to solve this problem is to plug in numbers for m in both expressions and compare them.
You know that m is a multiple of 3, so the least positive integer you can plug in for m is 3.
If \(m = 3\), then \(x^{m-3} =1\) and \(x^\frac{m}{3} =x\). Since x can be any positive number, its relationship to 1 cannot be determined from the information given. This example is sufficient to show that the relationship between \(\frac{x^m}{x^3}\) and \(x^{\frac{m}{3}}\) cannot be determined from the information given. The correct answer is Choice D.
