APPROACH #1: Matching operations
Given:
Quantity A: \(x^2\)
Quantity B: \(x^3\)

Since we can be certain that \(x^2\) is POSITIVE, we can safely divide both quantities by \(x^2\) to get:
Quantity A: \(1\)
Quantity B: \(x\)
Since we're told \(x<0\), we can be certain that Quantity A is greater.

Answer: A
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APPROACH #2: Properties of exponents
Two important rules:

ODD exponents preserve the sign of the base.
So, (NEGATIVE)^(ODD integer) = NEGATIVE
and (POSITIVE)^(ODD integer) = POSITIVE

An EVEN exponent always yields a positive result (unless the base = 0)
So, (NEGATIVE)^(EVEN integer) = POSITIVE
and (POSITIVE)^(EVEN integer) = POSITIVE

Since x is NEGATIVE, we know that \(x^3\) must be NEGATIVE (since 3 is an ODD exponent)
Conversely, we know that \(x^2\) must be POSITIVE (since 2 is an EVEN exponent)

We have:
Quantity A: POSITIVE
Quantity B: NEGATIVE

Answer: A


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