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(-1)^(-1/3)(-8)^(-1/3)(-27)^(-1/3)(-64)^(-1/3) =

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Joined: 02 Sep 2009
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(-1)^(-1/3)(-8)^(-1/3)(-27)^(-1/3)(-64)^(-1/3) = [#permalink]

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New post 10 Sep 2017, 05:25
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Difficulty:

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Question Stats:

59% (00:37) correct 41% (00:53) wrong based on 67 sessions

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\((-1)^{(-\frac{1}{3})}(-8)^{(-\frac{1}{3})}(-27)^{(-\frac{1}{3})}(-64)^{(-\frac{1}{3})} =\)


A. 24

B. 1/24

C. -1/24

D. -24

E. It cannot be determined from the information given.
[Reveal] Spoiler: OA

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Kudos [?]: 128915 [0], given: 12183

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(-1)^(-1/3)(-8)^(-1/3)(-27)^(-1/3)(-64)^(-1/3) = [#permalink]

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New post 10 Sep 2017, 09:39
Bunuel wrote:
\((-1)^{(-\frac{1}{3})}(-8)^{(-\frac{1}{3})}(-27)^{(-\frac{1}{3})}(-64)^{(-\frac{1}{3})} =\)


A. 24

B. 1/24

C. -1/24

D. -24

E. It cannot be determined from the information given.


Essentially the question: \((-1*-8*-27*-64)^{-\frac{1}{3}} = 1/(1*8*27*64)^{\frac{1}{3}}\)
This implies \(\frac{1}{(1*2*3*4)} = \frac{1}{24}\)
Option B

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Re: (-1)^(-1/3)(-8)^(-1/3)(-27)^(-1/3)(-64)^(-1/3) = [#permalink]

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New post 10 Sep 2017, 15:59
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Bunuel wrote:
\((-1)^{(-\frac{1}{3})}(-8)^{(-\frac{1}{3})}(-27)^{(-\frac{1}{3})}(-64)^{(-\frac{1}{3})} =\)


A. 24

B. 1/24

C. -1/24

D. -24

E. It cannot be determined from the information given.

If factoring out the negative exponent is unfamiliar, you can take a very traditional route (not too time-consuming -- I was under a minute and I checked accuracy with another method)

\((-1)^{(-\frac{1}{3})}(-8)^{(-\frac{1}{3})}(-27)^{(-\frac{1}{3})}(-64)^{(-\frac{1}{3})} =\)


\(\frac{1}{\sqrt[3]{-1}}\) * \(\frac{1}{\sqrt[3]{-8}}\) * \(\frac{1}{\sqrt[3]{-27}}\) * \(\frac{1}{\sqrt[3]{-64}}\) = **


\(\frac{1}{-1}\) * \(\frac{1}{-2}\) * \(\frac{1}{-3}\) * \(\frac{1}{-4}\)

Multiply the denominators. The answer will be positive because there are an even number of negative factors, that is (-)(-)(-)(-) = (+)

\(\frac{1}{24}\)

ANSWER B

** If thinking in fractional exponents is easier :-o , this stage of the expression could be written

\(\frac{1}{(-1)^{\frac{1}{3}}}\) * \(\frac{1}{(-8)^{\frac{1}{3}}}\) * \(\frac{1}{(-27)^{\frac{1}{3}}}\) * \(\frac{1}{(-64)^{\frac{1}{3}}}\)

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(-1)^(-1/3)(-8)^(-1/3)(-27)^(-1/3)(-64)^(-1/3) = [#permalink]

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New post 13 Sep 2017, 17:30
Option B

(-1)^(-1/3)(-8)^(-1/3)(-27)^(-1/3)(-64)^(-1/3)

Here \(\frac{-1}{3}\) indicates cube root and -ve means the number will go in denominator

-1 *\(\frac{1}{-2} *\frac{1}{-3}*\frac{1}{-4}\)

= \(\frac{1}{24}\)

Kudos [?]: 9 [0], given: 74

(-1)^(-1/3)(-8)^(-1/3)(-27)^(-1/3)(-64)^(-1/3) =   [#permalink] 13 Sep 2017, 17:30
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