Let p be a prime and let m and n be natural numbers. Prove that p | mn implies pn | mn. Attempt: Since mn can be written out as a product of primes i.e: p1p2...pn in which p is a divisor. Raising mn means that there would exist pn primes for each factor of m: mn = m1m2...mn = (p1...pn)1(p1...pn)2....(p1...pn)n = p1a1p2a2...pnan which means pn | mn. Is there anything I'm missing to clean it up? Cheers for the help.