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505-555 (Easy)|   Algebra|   Exponents|      
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Bunuel
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If 1/64^x = 4,096, x = 18 Mar 2020, 08:56
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D
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15% (low)

Question Stats:

80% (01:23) correct 20% (01:45) wrong based on 237 sessions

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If \((\frac{1}{64})^x = 4,096\), \(x =\)


A. -1/3

B. -1/2

C. \(-\sqrt{2}\)

D. -2

E. -3
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D
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tbhauer
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If 1/64^x = 4,096, x = 18 Mar 2020, 09:23
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This problem can be solved either by plugging in the possible values for x into the equation, or by taking the logarithm with base (1/64) of 4096 to isolate x on the left side of the equation. In this case, x=-2, so the answer is D.
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If 1/64^x = 4,096, x = 18 Mar 2020, 15:32
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2^6(-1*)=2^12
*=-2
hence, answer D Should be correct,

what level of difficulty is this
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If 1/64^x = 4,096, x = 18 Mar 2020, 23:47
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When I first looked at this question, the first thing that struck me was that 4096 and 64 are both powers of 2. I also knew that 4096 is the square of 64 / 64 is the square root of 4096.

Sometimes, knowing some such numbers by memory will not only cut down the time taken to solve a problem but can also lead you towards the right approach to solve the problem.

Knowing that 4096 is a square of 64 helps us understand that if we make the base as 64 on the both sides of the equation, we can then equate the powers.

Having said that, it is not a mandate that you have to memorise the squares of all numbers from 1 to 100 if you are preparing for the GMAT. If you can memorise squares till 40, you can use that as a springboard to find out squares of bigger numbers.

For example, if you knew that \(32^2\) = 1024, it’s not hard to figure out that \(64^2\) = 4*\(32^2\) (NO, it is not 2*\(32^2\), remember if x = 2y, \(x^2\)=4*\(y^2\)).
An alternative set of numbers that can help you solve this question is your knowledge of powers of 2. If you know that 4096 = \(2^{12}\) and 64 = \(2^6\), its not hard to figure out that 64 is the square root of 4096.

Also note that \(\frac{1}{x^n}\) = \(x^{-n}\) and \(1^n\) = 1.

\((\frac{1}{64})^x\) = \(\frac{1}{64^x}\) = \(64^{-x}\).

4096 = \(64^2\).

Since (\(\frac{1}{64^x}\)) = 4096, we have \(64^{-x}\) = \(64^2\). Since the bases are same, the exponents also have to be equal.
Therefore, -x = 2 or x=-2.

The correct answer option is D.

Hope that helps!
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If 1/64^x = 4,096, x = 19 Mar 2020, 09:14
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(1/64)^x= 4096=64*64

64^(-x)=64^2

=> -x=2
x= -2

ANS:D
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If 1/64^x = 4,096, x = 20 Mar 2020, 04:48
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Bunuel
If \((\frac{1}{64})^x = 4,096\), \(x =\)


A. -1/3

B. -1/2

C. \(-\sqrt{2}\)

D. -2

E. -3
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Simplifying, we have:

64^(-x) = 2^12

2^(-6x) = 2^12

-6x = 12

x = -2

Answer: D
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If 1/64^x = 4,096, x = 20 Oct 2023, 12:03
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