What is the prime factorization of 500 using exponents?

The prime factorization of 500 can be determined by breaking it down into its prime factors.

First, we can divide 500 by the smallest prime number, which is 2:

• 500 ÷ 2 = 250

Next, we divide 250 by 2 again:

• 250 ÷ 2 = 125

Since 125 is not divisible by 2, we move on to the next prime number, which is 3. However, 125 is not divisible by 3 either. The next prime number is 5:

• 125 ÷ 5 = 25

We can divide 25 by 5 again:

• 25 ÷ 5 = 5

Finally, we divide 5 by 5:

• 5 ÷ 5 = 1

Now we have broken down 500 into its prime factors:

• 2 (appears 2 times)
• 5 (appears 3 times)

So, we can write the prime factorization of 500 using exponents as:

500 = 2² × 5³