To express the whole number 125 as a product of prime numbers with exponents, we first need to find the prime factorization of 125. Here's how to do it:
Step 1: Start by dividing 125 by the smallest prime number, which is 2. Since 125 is not divisible evenly by 2, move on to the next prime number.
Step 2: Divide 125 by the next prime number, which is 3. Again, 125 is not divisible evenly by 3.
Step 3: Divide 125 by the next prime number, which is 5. This time, 125 is divisible evenly by 5. So, 125 divided by 5 is 25.
Step 4: Repeat the process with the quotient (25) from the previous step. Divide 25 by the smallest prime number, which is 2. Again, 25 is not divisible evenly by 2.
Step 5: Divide 25 by the next prime number, which is 3. Once again, 25 is not divisible evenly by 3.
Step 6: Divide 25 by the next prime number, which is 5. This time, 25 divided by 5 is 5.
Now, we have reached a prime number. 5 cannot be divided further since it is a prime number.
Hence, the prime factorization of 125 is 5 * 5 * 5, or in exponent form: 5^3.