Mathematics

Problem

For positive real numbers

x

and

y

, simplify the expression

E=\frac{\bigl(x^{\tfrac{1}{2}}y^{\tfrac{1}{3}}\bigr)^{6}}{\bigl(x^{2}y\bigr)^{\tfrac{3}{2}}}.

Present each step clearly, showing how you deal with the powers of

x

and

y

separately before writing the final simplified form of

E