(1)a^(1/2)*a^(1/4)*a^(-3/8)=a^[(1/2)+(1/4)-(3/8)]=a^(-3/8);
(2)[a^(1/2)*y(-1/3)]^6=a^[(1/2)*6]*y^[(-1/3)*6]=a³*y^(-2)=a³/y²;
(3)[8a^(-3)/27b^6]^(-1/3)=(8/27)^(-1/3)*a^[(-3)*(-1/3)]*b^[6*(-1/3)]=(2/3)ab^(-2)=2a/(3b²);
(4)2x^(-1/3)*[(1/2)x^(1/3)-2x^(-2/3)]=x^[(-1/3)+(1/3)]-4x^[(-1/3)+(-2/3)]=x^0-4x^(-1)=1-(1/x);