GIVEN: \(\frac{(10^3)(0.027)}{(900)(10^{-2})}=(3)(10^m)\)

Rewrite some values: \(\frac{(10^3)(27)(10^{-3})}{(9)(100)(10^{-2})}=(3)(10^m)\)

Rewrite more values: \(\frac{(10^3)(3^3)(10^{-3})}{(3^2)(10^2)(10^{-2})}=(3)(10^m)\)

Simplify: \(\frac{(10^0)(3^3)}{(3^2)(10^0)}=(3)(10^m)\)

Simplify: \(\frac{3^3}{3^2}=(3)(10^m)\)

Simplify: \(3=(3)(10^m)\)


This tells us that \(10^m = 1\), which means m = 0

We get:
QUANTITY A: 0
QUANTITY B: 3

Answer: B

Cheers,
Bret