Question 148092
If you have {{{y^(-1/2)}}}, you can rewrite this as {{{y^(-1/2)=1/y^(1/2)}}}. 



If  you have {{{1/y^(-1/2)}}}, you can rewrite this as {{{1/y^(-1/2)=y^(1/2)/1=y^(1/2)}}}. 


So to rewrite a term with a positive exponent, simply flip the fraction.




{{{(y^(3/4)/y^(-1/2))^8}}} Start with the given expression.



{{{(y^(3/4)y^(1/2))^8}}} Flip the fraction {{{1/y^(-1/2)}}} to get {{{y^(1/2)}}}. 



{{{(y^(3/4+1/2))^8}}} When you multiply monomials with a common base, you simply add the exponents.




{{{(y^(5/4))^8}}} Add the fractions.



{{{y^((5/4)8)}}} Multiply the inner and outer exponent.



{{{y^(40/4)}}} Multiply.



{{{y^(10)}}} Reduce.



So {{{(y^(3/4)/y^(-1/2))^8}}} simplifies to {{{y^(10)}}}



In other words, {{{(y^(3/4)/y^(-1/2))^8=y^(10)}}} where {{{y>0}}}