Given $\sigma,\tau \in S_7$ $$\sigma=(123456),\, \tau=(123)(456)$$ write $\sigma \circ\tau$ as a product of disjoint cycles.
Now, $\sigma \circ \tau$ is $(132465)$. To my understanding it doesn't make sense to ask to break a cycle into disjoint cycles, so I'd answer $(132465)(7)$—abusing the notation for a cycle with $(7)$. Is that correct?
Also, what would have happened if the length of the cycle was $7$, such as $(1234567)$? In that case, how can I write that cycle as a product of disjoint cycles?