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B
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Difficulty:
45%
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Question Stats:
71% (02:22) correct
29%
(02:49)
wrong
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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
A. 2
B. 5/2
C. 5
D. 25/4
E. 24
![Given 2^(4x) = 1600, what is the value of [2^(x-1)]^4](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "Given 2^(4x) = 1600, what is the value of [2^(x-1)]^4"){kind=icon}
17 Jun 2013, 06:17
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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
\(\frac{[2^{(x-1)}]^4}{[2^x]^2}=\frac{2^{4(x-1)}}{2^{2x}}=2^{4x-4-2x}=2^{2x-4}=\frac{2^{2x}}{16}\).
Since \(2^{4x} = 1600\), then \(2^{2x}=\sqrt{1600}=40\).
Therefore, \(\frac{2^{2x}}{16}=\frac{40}{16}=\frac{5}{2}\).
Answer: B.
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.
General Discussion
21 Mar 2017, 06:17
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fozzzy
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
