Express the following number as the product of prime factors:512

To express 512 as the product of prime factors, we need to perform a process called prime factorization.

Step 1: Start with 512. Step 2: Divide 512 by the smallest prime number, which is 2. 512 ÷ 2 = 256

Step 3: Continue dividing by 2. 256 ÷ 2 = 128 128 ÷ 2 = 64 64 ÷ 2 = 32 32 ÷ 2 = 16 16 ÷ 2 = 8 8 ÷ 2 = 4 4 ÷ 2 = 2 2 ÷ 2 = 1

Step 4: Since we reached 1, we stop here.

Now, count the number of times we divided by 2. We divided 512 by 2 a total of 9 times.

So, the prime factorization of 512 is:

512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

Which is:

512 = 2^9