JAMB 1995 · UME · Q6

Evaluate $\dfrac{81^{\frac34} - 27^{\frac13}}{3 \times 2^3}$ .

Worked solution (try it first)

$81^{\frac34}$ : take the fourth root, then cube.
$\sqrt[4]{81} = 3$ and $3^3 = 27$ .
$27^{\frac13}$ is the cube root of 27, which is 3.
So the top is $27 - 3 = 24$ .
The bottom is $3 \times 8 = 24$ , so the value is $\frac{24}{24} = 1$ , option B.