\(x=1, y=3,z=5\)

Quantity A	Quantity B
\(x^{-1}yz^{-2}\)	\((\frac{xz}{y})^{-2}\)

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.
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IMPORTANT CONCEPT #1: x^(-n) = 1/(x^n)
IMPORTANT CONCEPT #2: (x/y)^(-n) = (y/x)^n

Given:
Quantity A: [x^(-1)](y)[(z^(-2]
Quantity B: (xz/y)^(-2)

Apply rule #1 to Quantity A to get:
Quantity A: (1/x)(y)(1/z^2)
Quantity B: (xz/y)^(-2)

Apply rule #2 to Quantity B to get:
Quantity A: (1/x)(y)(1/z^2)
Quantity B: (y/xz)^2

Simplify to get:
Quantity A: y/(xz²)
Quantity B: y²/(x²z²)

Since z² is positive, we can multiply both quantities by z² to get:
Quantity A: y/x
Quantity B: y²/x²

Since x² is positive, we can multiply both quantities by x² to get:
Quantity A: xy
Quantity B: y²

Since y is positive, we can divide both quantities by y to get:
Quantity A: x
Quantity B: y

Since x=1 and y=3, the correct answer is B

Cheers,
Brent


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Brent Hanneson – Creator of greenlighttestprep.com

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