a)
(0,2^{\sqrt{6}})^{\sqrt{\frac{3}{2}}}=(0,2)^{\sqrt{\frac{18}{2}}}=0,2^{\sqrt9}=0,2^3=0,008
b)
3^{\sqrt3}* 27^{1-\sqrt3}=3^{\sqrt3}*(3^3)^{1-\sqrt3}=3^{\sqrt3}*3^{3-3\sqrt3}=3^{\sqrt3+3-\sqrt3}=3^{3-2\sqrt3}
c)
log_{2}32=5, bo 2^5=32
d)
log_{9}\sqrt3=x
9^x=\sqrt3
3^{2*x}=3^{\frac{1}{3}}
3^{2x}=3^{\frac{1}{3}}
2x=\frac{1}{3} |*3
6x=1 |:6
x=\frac{1}{6}