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If (-2)^(-4x) = (-64)^2, then what is the value of x?

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V
Joined: 02 Sep 2009
Posts: 49993
If (-2)^(-4x) = (-64)^2, then what is the value of x?  [#permalink]

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New post 03 Aug 2018, 04:41
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A
B
C
D
E

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  25% (medium)

Question Stats:

80% (01:04) correct 20% (01:09) wrong based on 45 sessions

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Director
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Joined: 01 Oct 2017
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WE: Supply Chain Management (Energy and Utilities)
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If (-2)^(-4x) = (-64)^2, then what is the value of x?  [#permalink]

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New post 03 Aug 2018, 04:57
Bunuel wrote:

GMAT Club Tests Fresh Question:



If \((-2)^{(-4x)} = (-64)^2\), then what is the value of x?

A. -4
B. -3
C. -2
D. 3
E. 4


\((-2)^{(-4x)} = (-64)^2\)
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)
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Re: If (-2)^(-4x) = (-64)^2, then what is the value of x?  [#permalink]

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New post 03 Aug 2018, 05:06
(-2)^(-4x) = (-64)^2
(-2)^2*(-2x) = (-4^3)^2
4^(-2x) = (4)^6
-2x = 6
x = -3

Hence, B.
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Re: If (-2)^(-4x) = (-64)^2, then what is the value of x?  [#permalink]

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New post 04 Aug 2018, 03:45
Bunuel wrote:

GMAT Club Tests Fresh Question:



If \((-2)^{(-4x)} = (-64)^2\), then what is the value of x?

A. -4
B. -3
C. -2
D. 3
E. 4



Note:

1. Base is negative
2. Exponents is even integer.

When you have negative base with even exponents , you can easily ignore it (Negative Sign).

Now the Equation has become :

\((2)^{-4x} = (2^6)^2\)

-4x = 12

x = -3.

The best answer is B.
GMAT Club Bot
Re: If (-2)^(-4x) = (-64)^2, then what is the value of x? &nbs [#permalink] 04 Aug 2018, 03:45
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If (-2)^(-4x) = (-64)^2, then what is the value of x?

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