If the product $\left({\mathrm{a}}^2\right)\times \left(2{\mathrm{a}}^{22}\right)\times \left(4{\mathrm{a}}^{26}\right)=k{a}^m$, then find the value of $k$.

If the product $\left(\frac{2}{3}\mathrm{xy}\right)\times \left(-\frac{9}{10}{\mathrm{x}}^2{\mathrm{y}}^2\right)=-\frac{3}{5}{x}^k{y}^3$

If the product $\left(-\frac{10}{3}{\mathrm{pq}}^3\right)\times \left(\frac{6}{5}{\mathrm{p}}^3\mathrm{q}\right)=-4p^k{q}^4$.

Then find the value of $k$.