You can use the prime factorization of a number, written

as the product of powers of prime numbers, to find
the number of factors the number has. First, express the
number as a product of powers of prime numbers; for
example, 36=2 to power 2 3 to power 3
Then increase each exponent by 1,
and find the product of these increased exponents. This
product is the number of factors of the number. In the
example for 36,(2+1)(2+1) so 36 has 9 factors.
how do i write 48 as a product of powers of prime numbers

To write 48 as a product of powers of prime numbers, we can use prime factorization. Here's how you can do it:

1. Start by dividing 48 by the smallest prime number, which is 2. You get 48 ÷ 2 = 24.
2. Now, divide 24 by 2 again. 24 ÷ 2 = 12.
3. Continue dividing the quotient by 2 until you can no longer divide evenly. You get 12 ÷ 2 = 6.
4. Now, divide the new quotient, 6, by the next smallest prime number, which is 3. You get 6 ÷ 3 = 2.
5. Finally, divide the last quotient, 2, by itself. You get 2 ÷ 2 = 1.

The prime factorization of 48 is 2^4 × 3^1. This means 48 can be written as the product of 2 raised to the power of 4 and 3 raised to the power of 1.

Therefore, 48 = 2^4 × 3^1.

Jessica, Chandice, and Thomas or whoever -- please post your attempts to answer these 8 questions.