Let the positive integer n be written in terms of powers of the prime p so that we have n...

Let the positive integer n be written in terms of powers of the prime p so that we have n = akpk + ⋯ + a2P2 + a1P + a0, where 0 ≤ ai < p. Show that the exponent of the highest power of p appearing in the prime factorization of n! is