Question

Find the value of $({81}^{1/2}\times 8^{2/3}\times {32}^{2/5}{)}^{1/2}$

Answer 1

Observe $81=3^4$. Hence
${81}^{1/2}=(3^4{)}^{1/2}=3^{4\times \left(1/2\right)}=3^2=9$.
Similarly,
$8^{2/3}=(2^3{)}^{2/3}=2^{3\times \left(2/3\right)}=2^2=4$,
${32}^{2/5}=(2^5{)}^{2/5}=2^{5\times \left(2/5\right)}=2^2=4$.
Thus we get
$({81}^{1/2}\times 8^{2/3}\times {32}^{2/5}{)}^{1/2}=(9\times 4\times 4{)}^{1/2}=(144{)}^{1/2}=\sqrt{144}=12$.