Find:

(i) $\left(9^{\smash{\frac{3}{2}}} \right)$

(ii) $\left(32^{\smash{\frac{2}{5}}} \right)$

(iii) $\left(16^{\smash{\frac{3}{4}}} \right)$

(iv) $\left(125^{\smash{\frac{-1}{3}}} \right)$

(i) $\left(9^{\smash{\frac{3}{2}}} \right)$

= (3²) ^3/2

= (3)³

= 3 x 3 x 3

= 27

Hence, $\left(9^{\smash{\frac{3}{2}}} \right)$ = 27

(ii) $\left(32^{\smash{\frac{2}{5}}} \right)$

= (2⁵) ^2/5

= (2)²

= 2 x 2

= 4

Hence, $\left(32^{\smash{\frac{2}{5}}} \right)$ = 4

(iii) $\left(16^{\smash{\frac{3}{4}}} \right)$

= (2⁴) ^3/4

= (2)³

= 2 x 2 x 2

= 8

Hence, $\left(16^{\smash{\frac{3}{4}}} \right)$ = 8

(iv) $\left(125^{\smash{\frac{-1}{3}}} \right)$

= (5³) ^-1/3

= (5)^-1

= $\dfrac{1}{5}$

Hence, $\left(125^{\smash{\frac{-1}{3}}} \right)$ = $\dfrac{1}{5}$