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If (n × n)^1/6 = ((64)^1/3)/2, what is the value of n?
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07 Apr 2022, 05:52
07 Apr 2022, 05:52
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If \((n * n)^{\frac{1}{6}} = \frac{64^{\frac{1}{3}}}{2}\), what is the value of n?
(A) 2
(B) 3
(C) 4
(D) 8
(E) 16
(A) 2
(B) 3
(C) 4
(D) 8
(E) 16
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Re: If (n × n)^1/6 = ((64)^1/3)/2, what is the value of n?
[#permalink]
07 Apr 2022, 05:52
07 Apr 2022, 05:52
1
Carcass wrote:
If \((n * n)^{\frac{1}{6}} = \frac{64^{\frac{1}{3}}}{2}\), what is the value of n?
(A) 2
(B) 3
(C) 4
(D) 8
(E) 16
(A) 2
(B) 3
(C) 4
(D) 8
(E) 16
Simplify the left side, and replace \(64\) with \(2^6\) to get: \((n^2)^{\frac{1}{6}} = \frac{(2^6)^{\frac{1}{3}}}{2}\)
Apply the Power of a Power law to both sides to get: \(n^{\frac{1}{3}} = \frac{2^2}{2}\)
Simplify the right side: \(n^{\frac{1}{3}} = 2\)
Raise both sides to the power of \(3\) to get: \((n^{\frac{1}{3}})^3 = 2^3\)
Simplify both sides to get: \(n = 8\)
Answer: D
gmatclubot
Re: If (n × n)^1/6 = ((64)^1/3)/2, what is the value of n? [#permalink]
07 Apr 2022, 05:52
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