Question

Find:

(i) ${64}^{\frac{1}{2}}$ (ii) ${32}^{\frac{1}{5}}$ (iii) ${125}^{\frac{1}{3}}$

Answer 1

i) $(64{)}^{\frac{1}{2}}$

Express $64$ in terms of $8$

$=(8^2{)}^{\frac{1}{2}}=8^{2\times \frac{1}{2}}=8^1=8$

ii) $(32{)}^{\frac{1}{5}}$

Express $32$ in terms of $2$

$=(2^5{)}^{\frac{1}{5}}=2^{5\times \frac{1}{5}}=2^1=2$

iii) $(125{)}^{\frac{1}{3}}$

Express $125$ in terms of $5$

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