Evaluate \(\left(\frac{81}{16}\right)^{\frac{-1}{4}}\times 2^{-1}\)
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Correct Answer: Option A
Explanation:
\(\left(\frac{81}{16}\right)^{\frac{-1}{4}}\times 2^{-1}=\frac{1}{\left(\frac{81}{16}\right)^{\frac{1}{4}}}\times \frac{1}{2}\\
=\left(\frac{16}{81}\right)^{\frac{1}{4}}\times \frac{1}{2}\\
=\left(\frac{2}{3}\right)^{4\times \frac{1}{4}}\\
=\frac{2}{3}\times \frac{1}{2}\\
=\frac{1}{3}\)
\(\left(\frac{81}{16}\right)^{\frac{-1}{4}}\times 2^{-1}=\frac{1}{\left(\frac{81}{16}\right)^{\frac{1}{4}}}\times \frac{1}{2}\\
=\left(\frac{16}{81}\right)^{\frac{1}{4}}\times \frac{1}{2}\\
=\left(\frac{2}{3}\right)^{4\times \frac{1}{4}}\\
=\frac{2}{3}\times \frac{1}{2}\\
=\frac{1}{3}\)