Simplify \(\sqrt[3]{(64r^{-6})^{\frac{1}{2}}}\)
A
\(\frac{r}{2}\)
B
2r
C
\(\frac{1}{2r}\)
D
\(\frac{2}{r}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\sqrt[3]{(64r^{-6})^{\frac{1}{2}}}\)
= \(((64r^{-6})^{1/_2})^{1/_3}\)
=\((64r^{-6})^{1/_6}\)
= (\(64)^{1/_6}(r^{-6})^{1/_6}\)
=\(\frac{2}{\text{r}}\)
Source: Myschool Past Questions Archive (Record #31496)