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03 Aug 2018, 04:41
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B
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Difficulty:
15%
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Question Stats:
79% (01:16) correct
21%
(01:21)
wrong
based on 306
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If \((-2)^{(-4x)} = (-64)^2\), then what is the value of x?
A. -4
B. -3
C. -2
D. 3
E. 4
M37-97
A. -4
B. -3
C. -2
D. 3
E. 4
M37-97
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06 Dec 2021, 07:36
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Official Solution:
If \((-2)^{(-4x)} = (-64)^2\), then what is the value of \(x\)?
A. \(-4\)
B. \(-3\)
C. \(-2\)
D. \(3\)
E. \(4\)
Because of even powers of both sides, \((-2)^{(-4x)} = (-64)^2\) is the same as:
\(2^{(-4x)} = 64^2\);
\(2^{(-4x)} = 2^{12}\);
\(-4x=12\);
\(x=-3\)
Answer: B
If \((-2)^{(-4x)} = (-64)^2\), then what is the value of \(x\)?
A. \(-4\)
B. \(-3\)
C. \(-2\)
D. \(3\)
E. \(4\)
Because of even powers of both sides, \((-2)^{(-4x)} = (-64)^2\) is the same as:
\(2^{(-4x)} = 64^2\);
\(2^{(-4x)} = 2^{12}\);
\(-4x=12\);
\(x=-3\)
Answer: B
General Discussion
03 Aug 2018, 04:57
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Bunuel
\((-2)^{(-4x)} = (-64)^2\)
Or, \(((-2)^4)^{-x}= ((-2)^6)^2\) (negative number raised to even power=positive number raised to even power)
Or, \((2^4)^{-x}=(2^6)^2\)
Or, \(2^{-4x}=2^{12}\)
Or, -4x=12
Or, x=-3
Ans. (B)
