Q:

If $\operatorname{ord}_ma=10$, find $\operatorname{ord}_ma^6$

If $\operatorname{ord}_ma=10$, find $\operatorname{ord}_ma^6$.  Justify you're answer. 
I'm not sure what I should say for my answer to be justified.   However, I expect $\operatorname{ord}_ma^6=5$, because $5\cdot 6=30$ and $10\mid 30$.
Like I said, no idea if this is how to go about solving this problem. 

A:

If $$ord_ma=d, ord_m(a^k)=\frac{d}{(d,k)}$$ (Proof @Page#95)
Here $$d=10,k=6\implies  ord_m(a^6)=\frac{10}{(10,6)}=\frac{10}2=5$$

