Find the prime factorization of 198, and write it in exponent form. Show your method.

198 = 2x3x3x11

so 198 = 2(11)(3^2)

To find the prime factorization of 198, we need to find its prime factors, which are the prime numbers that divide evenly into 198.

To start, we can divide 198 by the smallest prime number, which is 2. If 198 is divisible by 2, we divide it as many times as possible until we can no longer divide evenly.

198 ÷ 2 = 99

Now we have a new number, 99. Since 99 is an odd number, we move on to the next prime number, which is 3. Again, we divide 99 as many times as possible by 3.

99 ÷ 3 = 33

The new number is 33, which is still odd. We continue to divide by prime numbers until we reach 1.

33 ÷ 3 = 11

The number has reduced to 11, which is a prime number. Since 11 is already a prime, we no longer need to divide further. So the prime factorization of 198 is 2 × 3 × 3 × 11.

Now, we can write it in exponent form:

198 = 2^1 × 3^2 × 11^1