28.03.2023 - 14:44

What is the prime factorization of 125 using exponents?

Question:

What is the prime factorization of 125 using exponents?

Answers (1)
  • Luisa
    April 11, 2023 в 06:41

    The prime factorization of 125 using exponents is:

    125 = 5^3

    To find the prime factorization of 125, we need to factor it into its prime factors. We can start by dividing 125 by the smallest prime number, which is 2. However, 2 is not a factor of 125, so we move on to the next smallest prime number, which is 3. Again, 3 is not a factor of 125, so we move on to the next smallest prime number, which is 5.

    Since 5 is a factor of 125, we can divide 125 by 5 to get:

    125 ? 5 = 25

    Now we repeat the process with 25:

    25 ? 5 = 5

    Since we cannot divide 5 any further by any prime number other than itself (which is already a prime), we have reached the end of the process. We have found that 125 can be expressed as the product of its prime factors, which are all 5s.

    Therefore, we can write the prime factorization of 125 as 5^3, where the exponent 3 indicates that the prime factor 5 appears 3 times in the factorization.

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