On the exponent of geometric unipotent radicals of pseudo-reductive groups

Let $k'/k$ be a finite purely inseparable field extension and let $G'$ reductive $k'$-group. We denote by $G=\R_{k'/k}(G')$ the Weil restriction of across $k'/k$, pseudo-reductive group. This article gives bounds for exponent geometric unipotent radical $\RR_{u}(G_{\bar{k}})$ in terms invariants starting with case $G'=\GL_n$ applying these results to where is simple