Question

Find the prime factorization of 55 exponent 5 times 65 time 49 exponent 13 what is the correct answer?

Answer 1

So 55^5 times 65 times 49^13
so this means
55 times itself 5 times times 65 times 49 times itself 13 times or 
55 times 55 times 55 times 55 times 55 times 65 times 49 times 49 times 49 times 49 times 49 times 49 times 49 times 49 times 49 times 49 times 49 times 49 times 49
so factor each
rule of exponents

55^5
55=11 times 5
55^5=5^5 times 11^5
65=5 times 13
49=7 times 7
49^13=7^26

total multiplication is 5^5 times 5 times 11 times 13 times 7^26
5^5 times 5=5^6
so prime factorization is 
5^6 times 7^26 times 11 times 13