Show that $I=(X_{k_1}^{a_1},...,X_{k_s}^{a_s})$ is $(X_{k_1},...,X_{k_s})$-primary, where $I$ is the ideal generated by the monomials $X_{k_1}^{a_1},...,X_{k_s}^{a_s}$ .
I noticed that $$\sqrt{I}=\sqrt{({X_{i_1}}^{a_1},...,{X_{i_k}}^{a_k})}=\sqrt{({X_{i_1}}^{a_1})+...+({X_{i_k}}^{a_k})}=\sqrt{\sqrt{(X_{i_1})^{a_1}}+...+\sqrt{(X_{i_k})^{a_k}}}=\sqrt{(X_{i_1})+...+(X_{i_k})}=\sqrt{(X_{i_1},...,X_{i_k})}=(X_{i_1},...,X_{i_k}).$$ I have to show that $I$ is primary, i.e. if $u\cdot v\in I$ then $u\in I$ or $v\in (X_{k_1},...,X_{k_s})$.