JAMB 1989 · UME · Q5

Simplify $\left(\sqrt[3]{64r^{-6}}\right)^{\frac12}$ .

Worked solution (try it first)

Cube root first: $\sqrt[3]{64} = 4$ and $\sqrt[3]{r^{-6}} = r^{-2}$ , so the inside is $4r^{-2}$ .
The power $\frac12$ is a square root: $(4r^{-2})^{\frac12} = 2r^{-1}$ .
A negative index means one over: $2r^{-1} = \frac2r$ , option D.