4.
[tex]2(x^{3}y)^{2} = 2\cdot x^{3\cdot 2}\cdot y^{2} =2x^{6}y^{2}\\\\(2x^{2}y)^3} = 2^{3}\cdot x^{2\cdot3}\cdot y^{3}=8x^{6}y^{3}\\\\(2x^{3}y)^{2} = 2^{2}\cdot x^{3\cdot2}\cdot y^{2} = 4x^{6}y^{2}\\\\(2x)^{2}y^{3} = 2^{2}\cdot x^{2}\cdot y^{3} = 4x^{2}y^{3}[/tex]
[tex]x^{3}(2y)^{3} = x^{3}\cdot2^{3}\cdot y^{3} = 8x^{3}y^{3}\\\\2(xy)^{3} = 2\cdot x^{3}\cdot y^{3} = 2x^{3}y^{3}\\\\y^{2}(2x)^{3} = y^{2}\cdot2^{3}\cdot x^{3} = 8x^{3}y^{2}[/tex]
