This type of problem is known as prime factorization. To solve it you need to do a factor tree. To get started find any two number that multiply together to give you 243. For example 3 X 81 = 243.
243
/ \
3 81
Now, for any non-prime number you have on your "tree," find 2 numbers that multiply to give you that number:
243
/ \
3 81
/ \
9 9
Continue the process until you have only prime numbers in your tree:
243
/ \
3 81
/ \
9 9
/ \ / \
3 3 3 3
Once you have nothing left. Write out your prime numbers in a list. Count the number of each type of prime number you have and make it an exponent. For this example there are five 3s so it is 3 to the 5th power.
The prime factorization of 243 is 3[sup:1baxv5op]5[/sup:1baxv5op]