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

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Math Expert
Joined: 02 Sep 2009
Posts: 59588
If (-2)^(-4x) = (-64)^2, then what is the value of x?  [#permalink]

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03 Aug 2018, 04:41
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Difficulty:

25% (medium)

Question Stats:

74% (01:18) correct 26% (01:35) wrong based on 116 sessions

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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

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

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03 Aug 2018, 04:57
2
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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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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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.
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Re: If (-2)^(-4x) = (-64)^2, then what is the value of x?  [#permalink]

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14 Oct 2019, 23:22
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Re: If (-2)^(-4x) = (-64)^2, then what is the value of x?   [#permalink] 14 Oct 2019, 23:22
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# If (-2)^(-4x) = (-64)^2, then what is the value of x?

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