Laws Of Exponents For Real Numbers

Given number:

156

Goal: Find the sum of the exponents of the prime factors in the prime factorization of 156.

Step 1: Perform the prime factorization of 156.

Start by dividing 156 by the smallest prime number, 2:

156 ÷ 2 = 78

Now divide 78 by 2 again:

78 ÷ 2 = 39

39 is not divisible by 2, so move to the next prime number, 3:

39 ÷ 3 = 13

13 is a prime number, so the prime factorization of 156 is:

156 = 2² × 3 × 13

Step 2: Find the sum of the exponents of the prime factors.

The exponents in the prime factorization 2² × 3¹ × 13¹ are 2, 1, and 1.

The sum of the exponents is:

2 + 1 + 1 = 4

Answer: The sum of the exponents of the prime factors in the prime factorization of 156 is 4.