Prime factor of larger numbers by hand/simple calculator $12402^5$

Question

Trying to work out a prime number factorization (preparing myself for an upcoming exam).

We have worked a bit with prime number factorization and $\gcd$ during this semester.

I know how to approach factoring out a number that around $12402$ by hand/simple calculator (casio fx-82ex).

But how would I approach something like factoring $ 12402^5$? This will end up as $(2.933990039*10^{20})$ on my calculator making it hard to for example look on the last three digits and see what they are dividable by.

Are there any best practices in approaching a number of this size?

Regards, Petter

Answer 1

If the prime factorisation of $n$ is $$n = p_1^{e_1}\ldots p_r^{e_r},$$ then we have $$n^5=p_1^{5e_1}\ldots p_r^{5e_r}.$$