Chris is conducting a science experiment with fruit flies to see how the population increases over a three-week period. Chris begins his project with 6 fruit flies and notices that the number of fruit flies triples each week. At the end of the third week, 18 of the fruit flies have died.

a. Write and simplify a numeric expression that can be used to represent the number of fruit flies remaining after 3 weeks.


b. Use prime factorization to generate two equivalent numerical expressions representing the number of fruit flies remaining after 3 weeks.


c. Use order of operations to simplify each numerical expression to validate their equivalence.