Express 16,200 as a product of powers of prime numbers in the exponential form.

Sure, here are the steps to express 16,200 as a product of powers of prime numbers in the exponential form:

1. First, we need to find the prime factors of 16,200.

2. Start by dividing the number by the smallest prime number, which is 2. 16,200 ÷ 2 = 8,100.

3. Continue dividing by 2 until you can't anymore. 8,100 ÷ 2 = 4,050, 4,050 ÷ 2 = 2,025.

4. Now, 2,025 is not divisible by 2. So, we move to the next prime number, which is 3. 2,025 ÷ 3 = 675.

5. Continue dividing by 3 until you can't anymore. 675 ÷ 3 = 225.

6. Now, 225 is not divisible by 3. So, we move to the next prime number, which is 5. 225 ÷ 5 = 45, 45 ÷ 5 = 9.

7. Continue dividing by 5 until you can't anymore. 9 is not divisible by 5.

8. Now, 9 is not divisible by 5. So, we move to the next prime number, which is 7. But 9 is not divisible by 7. So, we move to the next prime number, which is 3. 9 ÷ 3 = 3, 3 ÷ 3 = 1.

9. Now, we have found all the prime factors of 16,200. They are 2, 3, and 5.

10. Count the number of times each prime number appears. We have 2 three times, 3 four times, and 5 two times.

11. Therefore, 16,200 can be expressed as a product of powers of prime numbers in the exponential form as 2^3 * 3^4 * 5^2.