On exponents of some varieties of linear algebras

The algebra $UT_s$ of upper triangular matrices of a size $s$ is considered. The equivalent conditions for the growth estimation are obtained for subvarieties in $var(UT_s)$, for varieties of Leibnitz algebras with nilpotent commutant, and for varieties of Leibniz–Poisson algebras with the identities $\{\{x_1,y_1\},\dots,\{x_n,y_n\}\}=0$, $\{x_1,y_1\}\cdot\ldots\cdot\{x_n,y_n\}=0$.