Evaluate \(\left(\frac{81}{16}\right)^{\frac{-1}{4}}\times 2^{-1}\)
A
1/3
B
3
C
6
D
1/6
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\left(\frac{81}{16}\right)^{\frac{-1}{4}}\times 2^{-1}\) = \(\frac{1}{\left(\frac{81}{16}\right)^{\frac{1}{4}}}\times \frac{1}{2}\)
= \(\left(\frac{16}{81}\right)^{\frac{1}{4}}\times \frac{1}{2}\)
= \(\left(\frac{2}{3}\right)^{4\times \frac{1}{4}}\)
=\(\frac{2}{3}\times \frac{1}{2}\)
= \(\frac{1}{3}\)
Source: Myschool Past Questions Archive (Record #9569)