6. Feladat
a.)
`(sqrtxsqrt(x^3))/(sqrt(x^7))=(sqrt(x^3))/sqrt(x^6)=1/sqrt(x^3)=1/(x*sqrtx)=1/(x*sqrtx)*sqrtx/sqrtx=(1sqrtx)/(xsqrtxsqrtx)=sqrtx/(x*x)=color(red)(sqrtx/x^2)`

b.)
`(root(3)(y^2))/(root(3)(y)root(3)(y^4))=(root(3)(y^2))/(root(3)(y*y^4))=(root(3)(y^2))/(root(3)(y^5))=1/(root(3)(y^3))=color(red)(1/y)`



7. Feladat
c.)
`(root(4)(a)root(4)(a^5))/(root(4)(a^3)root(4)(a^2)root(4)(a^-3))=(root(4)(a*a^5))/(root(4)(a^3*a^2*a^-3))=(root(4)(a^6))/(root(4)(a^2))=(sqrt(a^3))/(sqrta)=sqrt(a^2)=color(red)(a)`

d.)
`(root(3)(a^2b^-1)root(3)(a^-2b^4))/(root(3)(a^5b^-3)root(3)(a^-4b^-1))=(root(3)(a^2b^-1a^-2b^4))/(root(3)(a^5b^-3a^-4b^-1))=root(3)(b^4/a^2)/root(3)(1/(ab^3))=root(3)(b^4)/(1/root(3)(ab^3))=root(3)(b^7)/root(3)(a)=color(red)((b^2root(3)(b))/root(3)(a))`



8. Feladat
e.)
`(root(3)(a^-2)root(4)(a^3))/(sqrt(a^-3)root(6)(a^-5))=(a^(1/12))/(a^(-7/3))=a^(29/12)=root(12)(a^29)=color(red)(a^2root(12)(a^5))`

f.)
`(root(4)(a^-1b^3)root(6)(a^5b^-3))/(root(3)(a^4b^-2)sqrt(a^3b^-3))=(root(12)((a^-1b^3)^3)root(12)((a^5b^-2)^2))/(root(6)((a^4b^-2)^2)root(a)((a^3b^-3)^3))=root(12)(a^-3b^9a^10b^-6)/(root(6)(a^8b^-4a^9b^-9))=color(red)(root(12)(a^7b^3)/(a^2root(6)(a^5b^-13))`