Use a factor tree to find the prime factorization of 96 write the prime factorization using exponents
Sure! Let's use a factor tree to find the prime factorization of 96.
To start, we write down the number 96. Then we think of two numbers that multiply together to give us 96. One pair of numbers that come to mind is 6 and 16. So we can write:
96 = 6 x 16
Next, we examine the factors we wrote down and try to break them down further. Let's focus on 6 and 16 separately.
6 can be broken down further into 2 x 3, since both 2 and 3 are prime numbers:
6 = 2 x 3
16 can be broken down further into 2 x 2 x 2 x 2, or 2^4:
16 = 2^4
Now we put it all together, combining the prime factors we found:
96 = 6 x 16
= 2 x 3 x 2^4
To write it using exponents, we simply group the same prime factors together and write the exponent depending on how many times it appears:
96 = 2^5 x 3
So the prime factorization of 96, using exponents, is 2^5 x 3.