Question

Find:

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

Answer 1

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

Express $9$ in terms of $3$

$=(3^2{)}^{\frac{3}{2}}=3^{2\times \frac{3}{2}}=3^3=27$

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

Express $32$ in terms of $2$

$=(2^5{)}^{\frac{2}{5}}=2^{5\times \frac{2}{5}}=2^2=4$

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

Express $16$ in terms of $4$

$=(2^4{)}^{\frac{3}{4}}=2^{4\times \frac{3}{4}}=2^3=8$

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

Express $125$ in terms of $5$

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