simplify \(16^{\frac{-1}{2}}\times 4^{\frac{-1}{2}} \times 27^{\frac{1}{3}}\)
A
3/8
B
2/3
C
3/4
D
3/2
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(16^{\frac{-1}{2}}\times 4^{\frac{-1}{2}} \times 27^{\frac{1}{3}}\)
=\(\frac{1}{16^{\frac{1}{2}}}\times \frac{1}{4^{\frac{1}{2}}}\times 27^{\frac{1}{3}}\)
=\(\frac{1}{\sqrt{16}} \times \frac{1}{\sqrt{4}} \times \sqrt[3]{27}\)
=\(\frac{1}{4} \times \frac{1}{2} \times \frac{3}{1}\)
= \(\frac{3}{8}\)
Source: Myschool Past Questions Archive (Record #9263)