Writing a number as a product of primes in exponential form means to write the number as the product of prime numbers, where each prime has some exponent:
[tex]n = (\text{first prime})^{\text{some exponent}}\cdot (\text{second prime})^{\text{some other exponent}}\cdot \ldots[/tex]
Question 1:
The first option is ok, because you have a product of three primes (5, 7 and 13), and you gave to each prime a certain exponent (2, 1 and 1)
The second option is not ok, because 24 isn't prime
The third option is ok: 3 and 13 are primes, and you have exponents 2 and 1
The last option is not ok, because 4 isn't prime
Question 2:
120, 10 and 12 are not prime, so the first three options are not ok. The last option is the correct prime factorization of 120, because we write it as the product of 2, 3 and 5 (which are all primes) with exponents 2, 1 and 1.
