Question

За правильные решения дам в награду 30 б.

Answer 1

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