Express 194400 in exponential form

To express 194400 in exponential form, we first need to break it down into its prime factors.

1. Start by dividing 194400 by the smallest prime number, which is 2. The result is 97200.
2. Divide 97200 by 2 again to get 48600.
3. Continue dividing by 2 until you can't divide evenly anymore. After dividing by 2 five times, you get 6075.
4. Now, divide 6075 by the next prime number, 3. The result is 2025.
5. Divide 2025 by 3 again to get 675.
6. Continue dividing by 3 until you can't divide evenly anymore. After dividing by 3 four times, you get 25.
7. Now, divide 25 by the next prime number, 5. The result is 5.
8. Divide 5 by 5 again to get 1.

So, the prime factorization of 194400 is 2^8 * 3^4 * 5^2. This is the exponential form of 194400.