Question

Use a factor tree to find the prime factorization of 125. Write the prime factorization using exponents.

A. 3^5 • 1
B. 5^3
C. 5 • 2^5
D. 5^5

Answer 1

The prime factorization of 125 using exponents is 5^3 since 125 equals 5 multiplied by itself three times.

Step-by-step explanation:

To find the prime factorization of 125 using a factor tree, we start by recognizing that 125 is a cube of 5, as it is equal to 5 × 5 × 5. Therefore, the prime factorization of 125 can be written using exponents as 53. This is because exponentiation is a form of shorthand for repeated multiplication, and in this case, we are multiplying the number 5 by itself three times. The correct answer to the prime factorization of 125 using exponents is option B: 53.