Look at this problem. What is the prime factorization of 147?
Let us start with the first prime number, 2. Can we divide 147 evenly by 2? We cannot.
So, we should move on to the next prime number which is 3.
147 divide by 3 is equal to 49.
Then we try factoring 49 and find that 7 is the smallest prime number that works. So, 49 divided by 7 is equal to 7.
We are done because all the factors are prime numbers already.
So 147 is equal to 3 times 7 times 7.
In index form, 147 will be equal to 3 times 7 squared.