Answer: 800=2^4 x 5^2
Step-by-step explanation: To write 800 as a product of its prime factors, we need to find the prime numbers that can divide evenly into 800.
First, we divide 800 by the smallest prime number, 2:
800 ÷ 2 = 400
Next, we divide the quotient, 400, by 2 again:
400 ÷ 2 = 200
Next, we divide the quotient, 200, by 2 again:
200 ÷ 2 = 100
Next, we divide the quotient, 100, by 2 again:
100 ÷ 2 = 50
Now, we try dividing the quotient, 50, by the next prime number, 5:
50 ÷ 5 = 10
Finally, we divide the quotient, 10, by 2:
10 ÷ 2 = 5
At this point, we can see that 5 is a prime number and cannot be factored any further.
Therefore, the prime factorization of 800 is:
800 = 2 × 2 × 2 × 2 × 5 × 5
In exponential form, this can be written as:
800 = 2^4 × 5^2