Discrete math practice problems

prove whether true or false

If ${a}^{2}$ divides ${b}^{2}$, then ${a}^{3}$ divides ${b}^{4}$

I think it is false because it is true that if ${a}^{2}$ divides ${b}^{2}$ then a divides b ,

and also true that if ${a}^{2}$ divides ${b}^{2}$ then ${a}^{4}$ divides ${b}^{4}$.

could anyone check this one?

prove whether true or false

If ${a}^{2}$ divides ${b}^{2}$, then ${a}^{3}$ divides ${b}^{4}$

I think it is false because it is true that if ${a}^{2}$ divides ${b}^{2}$ then a divides b ,

and also true that if ${a}^{2}$ divides ${b}^{2}$ then ${a}^{4}$ divides ${b}^{4}$.

could anyone check this one?