How can you use the prime factorization of the powers of ten to find the prime factorization of 270,000?

Prime factorization is the process of finding the factors of a number and these factors must be of prime numbers.

27000 = 27 × 10000
27000 = 27 × 10⁴
27000 = 3 × 9 × 10⁴ [Here we have 3 as a prime number, but not '9' and '10', so we will keep breaking this down]
27000 = 3 ×3 × 3 × (2 × 5) ⁴ [Here we have all prime numbers]
27000 = 3³ × 2⁴ × 5⁴ 

the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.