Question 1011533
1.   {{{25^(1/4)*25^(-7/4)= 25^(1/4-7/4)=25^(-6/4)=25^(-3/2)=1/25^(3/2)=1/sqrt(25^3)=1/125}}}


2. {{{(x^8/y^4)^(3/4)=(x^8)^(3/4)/(y^4)^(3/4)=root(4,(x^8)^3)/root(4,(y^4)^3)=root(4,x^24)/root(4,y^12)=root(4,(x^6)^4)/root(4,(y^3)^4)=x^6/y^3}}}

3.

{{{(a^4b^8)^(-1/4)=1/(a^4b^8)^(1/4)=1/root(4,(a^4(b^2)^4))=1/ab^2}}}

4.
{{{(m^8/n^12)^(-1/4)=1/(m^8/n^12)^(1/4)=1/(root(4,(m^2)^4)/(root(4,(n^3)^4)))=root(4,(n^3)^4)/root(4,(m^2)^4)=n^3/m^2}}}