JAMB 2011 · UTME · Q6

Simplify $\left(\dfrac{16}{81}\right)^{\frac14} \div \left(\dfrac{9}{16}\right)^{-\frac12}$ .

Worked solution (try it first)

Fourth roots: $\left(\frac{16}{81}\right)^{\frac14} = \frac23$ , since $2^4 = 16$ and $3^4 = 81$ .
The negative index flips the fraction: $\left(\frac{9}{16}\right)^{-\frac12} = \left(\frac{16}{9}\right)^{\frac12}$
$= \frac43$ .
Divide by multiplying by the reciprocal: $\frac23 \times \frac34 = \frac12$ , option B.