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555-605 (Medium)|   Arithmetic|   Exponents|   Roots|      
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Bunuel
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(-1)^(-1/3)(-8)^(-1/3)(-27)^(-1/3)(-64)^(-1/3) = 10 Sep 2017, 05:25
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B
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35% (medium)

Question Stats:

68% (01:30) correct 32% (01:32) wrong based on 431 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.
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B
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(-1)^(-1/3)(-8)^(-1/3)(-27)^(-1/3)(-64)^(-1/3) = 10 Sep 2017, 09:39
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Bunuel
\((-1)^{(-\frac{1}{3})}(-8)^{(-\frac{1}{3})}(-27)^{(-\frac{1}{3})}(-64)^{(-\frac{1}{3})} =\)


A. 24

B. 1/24

C. -1/24

D. -24

E. It cannot be determined from the information given.
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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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(-1)^(-1/3)(-8)^(-1/3)(-27)^(-1/3)(-64)^(-1/3) = 10 Sep 2017, 15:59
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Bunuel
\((-1)^{(-\frac{1}{3})}(-8)^{(-\frac{1}{3})}(-27)^{(-\frac{1}{3})}(-64)^{(-\frac{1}{3})} =\)


A. 24

B. 1/24

C. -1/24

D. -24

E. It cannot be determined from the information given.
Show more
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) = 13 Sep 2017, 17:30
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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 *\(\frac{1}{-2} *\frac{1}{-3}*\frac{1}{-4}\)

= \(\frac{1}{24}\)
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(-1)^(-1/3)(-8)^(-1/3)(-27)^(-1/3)(-64)^(-1/3) = 01 Aug 2019, 00:08
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(-1)(-8)(-27)(-64)=x^-3 \implies \frac{1}{24}=x
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(-1)^(-1/3)(-8)^(-1/3)(-27)^(-1/3)(-64)^(-1/3) = 22 May 2025, 07:18
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↧↧↧ Detailed Video Solution to the Problem Series ↧↧↧



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

Since all terms are raised to the same power so we can multiply the terms and take the power common.

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

Getting rid of the negatives as we have 4 negative signs which when multiplied will become positive

=> \(( 1 * 8 * 27 * 64 )^{(-\frac{1}{3})}\)
=> \((1^3 * 2^3 * 3^3 * 4^3)^{(-\frac{1}{3})}\)

Taking power of 3 common
=> \((1 * 2 * 3 * 4)^{3 * (-\frac{1}{3})}\)
=> \((1 * 2 * 3 * 4)^{-1})\)
=> \((24)^{-1})\)
=> \(\frac{1}{24}\)
=> \(x^2\) = 9x - 6x - 9 = 3x - 9

So, Answer will be B
Hope it helps!

Watch the following video to MASTER Roots

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