Question 104701
{{{(2x^(3/4)*y^(-1/2))^(-8)}}}
Use the following exponentiation rule, 
{{{(x^m*y^n)^p=x^(m*p)*y^(n*p)}}}
{{{(2x^(3/4)*y^(-1/2))^(-8)=(2)^(-8)*x^((3/4)*-8)*y^((-1/2)*(-8))}}}Distribute the exponent. 
{{{(2x^(3/4)*y^(-1/2))^(-8)=(2)^(-8)*x^(-6)*y^(4)}}}Multiply the exponents. 
{{{(2x^(3/4)*y^(-1/2))^(-8)=y^(4)/((2)^(8)*x^(6))}}}Only positive exponents wanted. 
{{{(2x^(3/4)*y^(-1/2))^(-8)=y^(4)/(256x^(6))}}}Expanded answer.