За правильные решения дам в награду 30 б.

1) $\frac{12^{1/2}}{7^{2/3}*8^{1/2}}* \frac{3^{1/2}*7^{5/3}}{8^{-1/6}} =3^ {\frac{1}{2}}*4^{ \frac{1}{2} }*7^{ -\frac{2}{3} }*8^{- \frac{1}{2} }* 3^ {\frac{1}{2}}*7^{\frac{5}{3} }*8^{ \frac{1}{6} }=$
$=3*2*7^{\frac{5-2}{3} }*2^{- \frac{3}{2} }*2^{ \frac{3}{6} }=3*2*7*2^{-1}=3*7=21$

2) $\frac{a^{3/4}+a^{1/2}*b^{1/4}}{a^{1/4}+b^{1/4}} = \frac{a^{1/2}*(a^{1/4}+b^{1/4})}{a^{1/4}+b^{1/4}} =a^{1/2}= \sqrt{a} = \sqrt{4} =2$

3) $(27^{1/2}*( \frac{1}{9} )^{3/4})^{4/3}=(27^{1/2})^{4/3}*(( \frac{1}{9} )^{3/4})^{4/3}=(3^3)^{2/3}* \frac{1}{9} = \frac{3^2}{9} =1$