Write the product $x^2yx^{-1}y^{-1}x^3y^3$ in the form $x^iy^j$ in the dihedral group $D_n$.
I used the fact that the dihedral group is generated by two elements $x$ and $y$ such that: $y^n=1$, $x^2=1$ and $xy=y^{-1}x$
and I found that $x^2yx^{-1}y^{-1}x^3y^3=y^5$
Is it correct ?