JAMB 2010 · UTME · Q7

Evaluate $\left(\dfrac{81}{16}\right)^{-\frac14} \times 2^{-1}$ .

Worked solution (try it first)

A negative index turns the fraction upside down: $\left(\frac{81}{16}\right)^{-\frac14} = \left(\frac{16}{81}\right)^{\frac14}$ .
Take fourth roots: $\sqrt[4]{16} = 2$ and $\sqrt[4]{81} = 3$ , so this is $\frac23$ .
$2^{-1} = \frac12$ , so the value is $\frac23 \times \frac12 = \frac13$ , option A.