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

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Math Expert
Joined: 02 Sep 2009
Posts: 46167

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10 Sep 2017, 05:25
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Difficulty:

35% (medium)

Question Stats:

67% (00:55) correct 33% (00:51) wrong based on 153 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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10 Sep 2017, 09:39
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1
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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10 Sep 2017, 15:59
1
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 (-)(-)(-)(-) = (+)

$$\frac{1}{24}$$

** If thinking in fractional exponents is easier , 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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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 *$$\frac{1}{-2} *\frac{1}{-3}*\frac{1}{-4}$$

= $$\frac{1}{24}$$
(-1)^(-1/3)(-8)^(-1/3)(-27)^(-1/3)(-64)^(-1/3) =   [#permalink] 13 Sep 2017, 17:30
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