Question

Evaluate:
(i) (25)^3/2
(ii) (32)^2/5
(iii) (81)^3/4

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right){\left(25\right)}^{\frac{3}{2}}=5^{2\times \frac{3}{2}}=5^3=125\left[(a^m{)}^n=a^{mn}\right] \\ \left(\mathrm{ii}\right){\left(32\right)}^{\frac{2}{5}}={\left(2^5\right)}^{\frac{2}{5}}=2^{5\times \frac{2}{5}}=2^2=4 \\ \left(\mathrm{iii}\right){\left(81\right)}^{\frac{3}{4}}={\left(3^4\right)}^{\frac{3}{4}}=3^{4\times \frac{3}{4}}=3^3=27 \end{gathered}$$