\(x < 0\)

Quantity A	Quantity B
\(x^5\)	\(x^4\)

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.

Explanation

If x < 0, then \(x^5\) < 0 and \(x^4\) > 0. Thus \(x^5\) < \(x^4\) , and the correct answer is Choice B.

Another approach:
Quantity A: x⁵
Quantity B: x⁴

Since we're told that x < 0, we can be certain that x ≠ 0.
From this, we can conclude that x⁴ is POSITIVE, which means we can divide both quantities by x⁴ to get:
Quantity A: x
Quantity B: 1

Since we're told that x < 0 (i.e., x is NEGATIVE), we can be certain that 1 is greater than x

Answer:

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