For convenience. Sometimes larger numbers have a lot of repeated factors.
Yes.
19 is a prime number in its own right and needs no exponents
11 is a prime number in its own right and needs no exponents
11 is already prime. No factorization or exponents needed.
47 is a prime number.
11 is a prime number.
2^5
41 is a prime number.
Write the prime factorization with exponents. Add 1 to each exponent. (Numbers without exponents actually have the exponent 1.) Multiply them together. That will be the number of factors.
19 is a prime number so the factorization is 1 x 19
None. 887 is a prime number.
2^3*3