Hi

I hope my reasoning is fine.
Quantity A:
(X)^-1 which is 1/1 then 1
Y = 3
And Z^-2 which gives us 1/25
We have (1)(3)/25 = 3/25

Quantity B
(XZ/Y)^-2 (remember PEMDAS)
So (5/3)^-2
Reciproqual to erase the minus.
(3/5)^2 which gives us 9/25.
We can compare them since they have the same denominator.
Quantity B is greater !

I hope I did not make any mistake

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


RELATED VIDEO FROM OUR COURSE

_________________

Notice that x,y,z are >0
A:
y/x*z^2
B:
y^2/x^2*z^2

multiple both the sides by x^2*z^2/ y^2 (as all terms are >0)

A:
x/y
B:
1

x<y

=> x/y is <1

therefore quantity B is greater.

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