Question

Simplify $\frac{(16a^2{)}^{\frac{1}{2}}\times (36a^4{)}^{\frac{-1}{2}}}{2a^{\frac{1}{2}}\times 5a^{\frac{3}{2}}\times 8a^{\frac{9}{4}}}$

Answer 1

$\frac{(16a^2{)}^{\frac{1}{2}}\times (36a^4{)}^{\frac{-1}{2}}}{2a^{\frac{1}{2}}\times 5a^{\frac{3}{2}}\times 8a^{\frac{9}{4}}}$
$=\frac{\text{/}4a\times \frac{1}{6a^2}}{2\sqrt{a}\times 5\sqrt{9^3}\times \text{/}{8}_2\sqrt[4]{4a^a}}=\frac{\frac{1}{a}}{12\times a^{\frac{1}{2}}\times a^{\frac{3}{2}}\times a^{\frac{9}{4}}}=\frac{1}{12}\left(\frac{1}{a(1+\frac{1}{2}+\frac{3}{2}+\frac{9}{4})}\right)-\frac{1}{12}\frac{1}{a^{\left(\frac{4+216+9}{4}\right)}}=\frac{1}{12}\left(\frac{1}{a^{\frac{21}{4}}}\right)$