[tex](2xy^{2})^{3} = (2xy^{2})(2xy^{2})(2xy^{2})[/tex]
Now, we can just multiply it and obtain the result
[tex](2xy^{2})(2xy^{2})(2xy^{2})=(4x^{2}y^{4})(2xy^{2})=8x^{3}y^{6} [/tex]
I used law presented on this example
[tex]2^{3}*2=2^{3}*2^{1}=2^{3+1}=2^{4}[/tex]