Determine the remainder we get if we divide $799^{801}$ by $264$

Question

Determine the remainder we get if we divide $799^{801}$ by $264$.
I need clear steps.

Answer 1

$799\equiv7\pmod{264},799^n\equiv7^n$ for integer $n\ge0$

Using Carmichael Function, $\lambda(264)=$lcm$(\lambda(3),\lambda(8),\lambda(11))=10$

As $(7,264)=1$

$$\implies7^{801}\equiv7^{801\pmod{10}}\equiv7^1\pmod{264}$$