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What is (1/16)^(-1/4) (m25#11)

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What is (1/16)^(-1/4) (m25#11) [#permalink]

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New post 15 Feb 2012, 06:45
What is \((\frac{1}{16})^{-\frac{1}{4}}\) ?

(A) \(-\frac{1}{2}\)
(B) \(2\)
(C) \(256^2\)
(D) \(\frac{1}{2}\)
(E) \(4\)
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Kudos [?]: 979 [0], given: 334

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Magoosh GMAT Instructor
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Joined: 28 Dec 2011
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Re: What is (1/16)^(-1/4) (m25#11) [#permalink]

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New post 17 Feb 2012, 12:26
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Hi, there! I'm happy to help with this. :)

What is (1/16)^(-1/4)
(A) -1/2
(B) 2
(C) 256^2
(D) 1/2
(E) 4


Well, this one combines a few good exponent rules.

First of all:

(any positive number)^(any power at all) = a positive number

so, right away, answer (A) is out.

One BIG idea --- a negative exponent means: take the reciprocal.

a^(-n) = 1/(a^n)

(1/a)^(-n) = a^n

Thus, (1/16)^(-1/4) = 16^(1/4)

Another BIG idea --- a fractional exponent means take a root.

a^(1/2) = the square root of a
a^(1/3) = the cube root of a
a^(1/4) = the fourth root of a

So, 16^(1/4) equals the fourth root of 16. What number, when raised to the fourth power, equals 16? That number is 2, because 2^4 = 2x2x2x2 = 16.

[Reveal] Spoiler:
Thus, Answer = B


Here's a challenging practice PS on laws of exponents

http://gmat.magoosh.com/questions/725

The question at that link should be followed by a complete video solution when you submit your answer.

Does all this make sense? Please let me know if you have any questions.

Mike :)
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Mike McGarry
Magoosh Test Prep

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Kudos [?]: 8456 [5], given: 102

Re: What is (1/16)^(-1/4) (m25#11)   [#permalink] 17 Feb 2012, 12:26
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