Question

Simplify:
$\left(i\right)(8^{\frac{2}{3}}{)}^{-\frac{3}{2}}$
$\left(ii\right)({64}^{\frac{2}{3}}{)}^{\frac{1}{2}}$
$\left(iii\right)({216}^{\frac{2}{3}}{)}^{\frac{1}{2}}$ [3 MARKS]

Answer 1

Application: 1 Mark each

$\left(i\right)(8^{\frac{2}{3}}{)}^{\frac{-3}{2}}=8^{\frac{2}{3}\times \frac{-3}{2}}$
$=8^{-1}$
$=\frac{1}{8}$

$\left(ii\right)({64}^{\frac{2}{3}}{)}^{\frac{1}{2}}={64}^{\frac{2}{3}\times \frac{1}{2}}$
$={64}^{\frac{1}{3}}=(4^3{)}^{\frac{1}{3}}$
$=4^{3\times \frac{1}{3}}$
$=4^1$
$=4$


$\left(iii\right)({216}^{\frac{-3}{2}}{)}^{\frac{1}{2}}={216}^{\frac{2}{3}\times \frac{1}{2}}$
$={216}^{\frac{1}{3}}$
$=(6^3{)}^{\frac{1}{3}}$
$=6^{3\times \frac{1}{3}}$
$=6^1$
$=6$