# 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.

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?
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kamphundg4
Explanation:
if a divides b then ${a}^{3}$ divides ${b}^{3}$. If ${a}^{3}$ divides ${b}^{3}$ then ${a}^{3}$ divides $b\ast {b}^{3}$ so ${a}^{3}$ divides ${b}^{4}$