NECO 2022 · Paper 1 · Q14

Evaluate $\left(\dfrac{256}{81}\right)^{-\frac{3}{4}}$ .

Worked solution (try it first)

A negative power turns the fraction upside down: $\left(\dfrac{81}{256}\right)^{\frac{3}{4}}$ .
Take the fourth root: $\sqrt[4]{81} = 3$ and $\sqrt[4]{256} = 4$ , giving $\frac{3}{4}$ .
Cube it: $\left(\frac{3}{4}\right)^3 = \frac{27}{64}$ , option D.