Find the prime factorization of 196, using exponents when repeated factors appear
196 = 14^2 = 2^2 7^2
To find the prime factorization of 196 using exponents, we will start by dividing it by the smallest prime number, which is 2.
1. First, we divide 196 by 2: 196 ÷ 2 = 98.
2. Since 98 is also divisible by 2, we divide again: 98 ÷ 2 = 49.
3. We cannot divide 49 by 2 anymore, so we move on to the next prime number, which is 3.
4. 49 is not divisible by 3, so we continue to the next prime number, which is 5.
5. 49 is not divisible by 5 either, so we move to the next prime number, which is 7.
6. Finally, 49 is divisible by 7: 49 ÷ 7 = 7.
7. At this point, we have obtained all prime factors.
Now, let's write the prime factorization of 196:
196 = 2^2 × 7^2
The exponent of 2 is 2 because we divided 196 by 2 twice, and the exponent of 7 is also 2 because we divided 196 by 7 once.