3. $\left(\dfrac{b^2}{a}\right)^{-2}.\left(\dfrac{a^2}{b}\right)^{-3}$
$=\dfrac{b^{-4}}{a^{-2}}.\dfrac{a^{-6}}{b^{-3}}$
$=\dfrac{b^{-1}}{a^{-4}}=\dfrac{1}{a^4b}$
4. $\dfrac{(\sqrt[3]{4a})^2}{\sqrt[6]{4a}}$
$=\dfrac{(4a)^{\frac{2}{3}}}{(4a)^{\frac{1}{6}}}$
$=(4a)^{\frac{1}{2}}=2\sqrt a$
5. $\dfrac{a^{\frac{4}{3}}(a^{\frac{-1}{3}}+a^{\frac{2}{3}})}{a^{\frac{1}{4}}(a^{\frac{3}{4}}+a^{\frac{-1}{4}})}$
$=\dfrac{a+a^2}{a+1}=a$