Discussion
Cube of \(-\frac{1}{4}\) is
Answer: B
The cube is \(-\frac{1}{64}\).
Cube the numerator and the denominator, keeping track of the sign. A negative number raised to an odd power stays negative:
\[ \begin{aligned} \left(-\tfrac{1}{4}\right)^{3} &= -\frac{1^{3}}{4^{3}} \\ &= -\frac{1}{64} \end{aligned} \]
\(\frac{1}{64}\) loses the sign, which would be right only for an even power. \(\pm\frac{1}{16}\) is the square, \(4^{2} = 16\), not the cube.
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