Simplify \(\sqrt[3]{\frac{27a^{-9}}{8}}\).
A
\(\frac{9a^2}{2a^3}\)
B
\(\frac{3}{2a^3}\)
C
\(\frac{2}{3a^2}\)
D
\(\frac{3a^2}{2}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\sqrt[3]{\frac{27a ^{-9}}{8}}\) = \(\frac{3a^{-3}}{2}\)
= \(\frac{3}{2}\) x \(\frac{1}{a^3}\)
= \(\frac{3}{2a^3}\)
Source: Myschool Past Questions Archive (Record #32476)