The prime factorization of a certain number is 2 to the 3rd power times 3 times 5 to the second power what is the number and how did you get it

The prime factorisation of a number is just writing how many prime numbers (numbers only divisible by 1 or themselves) go into a number.
First, we can write out the value of each number with an indicie:

Next, we replace the numbers with indicies in the question with their values:
8×3×25
Now, just multiply these numbers together to get your
8×3×25=600
So, the number is 600