Quantity A	Quantity B
\(80^{\frac{1}{3}}\)	\(270^{\frac{1}{3}}- 10^{\frac{1}{3}}\)

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.





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Sandy
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IMPORTANT RULE:(ab)^y = (a^y)(b^y)
For example, 12^17 = (4^17)(3^17)

Given:
Quantity A: 80^(1/3)
Quantity B: 270^(1/3) - 10^(1/3)

Apply law to get:
Quantity A: [10^(1/3)][8^(1/3)]
Quantity B: [27^(1/3)][10^(1/3)] - 10^(1/3)

Factor out 10^(1/3) in quantity B to get:
Quantity A: [10^(1/3)][8^(1/3)]
Quantity B: [10^(1/3)][27^(1/3) - 1]

Divide both quantities by 10^(1/3) to get:
Quantity A: 8^(1/3)
Quantity B: 27^(1/3) - 1

Evaluate both quantities to get:
Quantity A: 2
Quantity B: 3 - 1

Answer:
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Brent Hanneson – Creator of greenlighttestprep.com

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In the step before that, we have: Quantity B: [27^(1/3)][10^(1/3)] - 10^(1/3)

This similar to the expression xy - y
With this expression, we can factor out the y to get: xy - y = y(x - 1)

Likewise, in the original expression, we can factor out 10^(1/3) to get: [27^(1/3)][10^(1/3)] - 10^(1/3) = [10^(1/3)][27^(1/3) - 1]

Does that help?

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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