Use a factor tree to find the prime factors of 72. Write the prime factorization using exponents ?

To find the prime factorization of 72 using a factor tree, follow these steps:

Start by dividing 72 by the smallest prime number, which is 2.
72 ÷ 2 = 36
So, 72 = 2 × 36.

Now, divide 36 by 2 again.
36 ÷ 2 = 18
So, 72 = 2 × 2 × 18.

Next, divide 18 by 2.
18 ÷ 2 = 9
So, 72 = 2 × 2 × 2 × 9.

Now, divide 9 by the smallest prime number, which is 3.
9 ÷ 3 = 3
So, 72 = 2 × 2 × 2 × 3 × 3.

Finally, divide 3 by 3 to reach a prime number.
3 ÷ 3 = 1
So, 72 = 2 × 2 × 2 × 3 × 3 × 1.

Now, we can express the prime factorization using exponents:

72 = 2³ × 3².

So, the prime factorization of 72 is 2³ × 3².