00:01
In this problem, we're being asked to explain why the following expression, 2 squared times 13 to the 3rd times 9 squared, is not a prime factorization.
00:10
So, remember, prime factorization means that all of our bases in this case have to be prime numbers.
00:16
So let's start with the first expression.
00:17
We have 2 to the 2nd power, so our base is 2.
00:20
Well, 2 is a prime number because, remember, the definition of a prime number says that its only factors are 1 and itself.
00:26
And the only numbers that multiply to 2 are 1 and 2, so 2 is a prime number.
00:30
So this part's all set.
00:32
Now, for the second part, we have 13 to the 3rd power, so our base is 13.
00:36
13 is also a prime number, its only factors are 1 and 13, so this part's okay too...