Question

Find:
(i) $9^{\frac{3}{2}}$
(ii) ${32}^{\frac{2}{5}}$
(iii) ${16}^{\frac{3}{4}}$
(d) ${125}^{\frac{-1}{3}}$

Answer 1

(1) $9^{\frac{3}{2}}$

$={\left(3^2\right)}^{\frac{3}{2}}$

$={\left(3\right)}^{2\times \frac{3}{2}}$

$=3^3$

$=27$

(2) ${32}^{\frac{2}{5}}$

$={\left(2^5\right)}^{\frac{2}{5}}$

$={\left(2\right)}^{5\times \frac{2}{5}}$

$=2^2$

$=4$

(3) ${16}^{\frac{3}{4}}$

$={\left(2^4\right)}^{\frac{3}{4}}$

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

$=2^3$

$=8$

(4) ${125}^{\frac{-1}{3}}$

$={\left(5^3\right)}^{\frac{-1}{3}}$

$={\left(5\right)}^{3\times \frac{-1}{3}}$

$=5^{-1}$

$=\frac{1}{5}$