Given the expression:
[tex](xy^3)^2(x^2y)^{-1}[/tex]
for the left factor, we can multiply the exponents to get the following:
[tex](xy^3)^2=x^2y^{3\cdot2}=x^2y^6[/tex]
and the right factor can be written like this:
[tex](x^2y)^{-1}=\frac{1}{x^2y}[/tex]
if we combine these results on the original expression, we get:
[tex](xy^3)^2(x^2y)^{-1}=(x^2y^6)\cdot\frac{1}{x^2y}=\frac{x^2y^6}{x^2y}=y^5[/tex]
therefore, the simplified expression is y⁵
