WAEC 2020 · Paper 1 · Q3

Simplify $\left[\left(\frac{16}{9}\right)^{-\frac32} \times 16^{-\frac34}\right]^{\frac13}$ .

Worked solution (try it first)

The negative index flips the fraction: $\left(\frac{16}{9}\right)^{-\frac32} = \left(\frac{9}{16}\right)^{\frac32}$ .
The square root is $\frac34$ , and cubing gives $\frac{27}{64}$ .
$16^{-\frac34} = \frac{1}{16^{\frac34}}$ .
The fourth root of 16 is 2, and $2^3 = 8$ , so this is $\frac18$ .
Multiply: $\frac{27}{64} \times \frac18 = \frac{27}{512}$ .
Cube root: $\sqrt[3]{27} = 3$ and $\sqrt[3]{512} = 8$ , so the value is $\frac38$ , option C.