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Given 2^(4x) = 1600, what is the value of [2^(x-1)]^4

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Given 2^(4x) = 1600, what is the value of [2^(x-1)]^4  [#permalink]

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New post Updated on: 17 Jun 2013, 05:18
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Difficulty:

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Question Stats:

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Given \(2^{4x} = 1600\), what is the value of \(\frac{[2^{(x-1)}]^4}{[2^x]^2}\)

A. 2
B. 5/2
C. 5
D. 25/4
E. 24

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Originally posted by fozzzy on 17 Jun 2013, 05:07.
Last edited by Bunuel on 17 Jun 2013, 05:18, edited 1 time in total.
Edited the question.
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Re: Given 2^4x = 1600, what is the value of [2^(x-1)]^4 / [2^x]^  [#permalink]

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New post 17 Jun 2013, 05:17
3
4
Given \(2^{4x} = 1600\), what is the value of \(\frac{[2^{(x-1)}]^4}{[2^x]^2}\)

A. 2
B. 5/2
C. 5
D. 25/4
E. 24

\(\frac{[2^{(x-1)}]^4}{[2^x]^2}=\frac{2^{4(x-1)}}{2^{2x}}=2^{4x-4-2x}=2^{2x-4}=\frac{2^{2x}}{16}\).

Since \(2^{4x} = 1600\), then \(2^{2x}=\sqrt{1600}=40\).

Therefore, \(\frac{2^{2x}}{16}=\frac{40}{16}=\frac{5}{2}\).

Answer: B.
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Re: Given 2^(4x) = 1600, what is the value of [2^(x-1)]^4  [#permalink]

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New post 21 Mar 2017, 05:17
fozzzy wrote:
Given \(2^{4x} = 1600\), what is the value of \(\frac{[2^{(x-1)}]^4}{[2^x]^2}\)

A. 2
B. 5/2
C. 5
D. 25/4
E. 24


We can simplify the question:

2^(4x - 4)/2^(2x)

2^(4x - 4 - 2x)

2^(2x - 4)

2^(2x)/2^4

We know that 2^4 = 16, and notice that 2^(2x) = √2^(4x). Thus

√2^(4x) = √1600

2^(2x) = 40

Thus, 2^(2x)/2^4 = 40/16 = 5/2.

Answer: B
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Re: Given 2^(4x) = 1600, what is the value of [2^(x-1)]^4  [#permalink]

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Re: Given 2^(4x) = 1600, what is the value of [2^(x-1)]^4 &nbs [#permalink] 12 Apr 2018, 06:15
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