How do you write the prime factorization of 100 using exponents?

Answer 1

List each prime factor in a multiplication statement, then raise them to a power however many times are necessary to make the number.

E.g. the prime factors of 120 are 2, 3 and 5. Listing these in a multiplication statement is 2 x 3 x 5. Giving each a power so the product will equal the number makes the statement 23 x 3 x 5.

Answer 2

Exponents are just a way of keeping track of repeated prime factors. The prime factorization of 900 is 2 x 2 x 3 x 3 x 5 x 5. This can also be written as 22 x 32 x 52

The higher the number, the more useful this becomes.

Answer 3

First, find the prime factorization in the usual way. Then, combine prime factors that are the same - simply write them once, count how many there are, and write the corresponding exponent. For example, the prime factorization of 72 is 2 x 2 x 2 x 3 x 3. Since the "2" appears three times, you write this part as 23; since the "3" appears twice, you write this part as 32. The final result is 23 x 32.

Answer 4

2 x 2 x 2 x 3 x 3 x 3 = 216

23 x 33 = 216

Answer 5

No prime power exists since there are no duplicate prime numbers in the prime factorization.

Answer 6

2 x 2 x 2 x 3 x 3 is the prime factorization of 72.

Using exponents, that can be expressed as 2^3 x 3^2 = 72.

Answer 7

Exponents are just shorthand for repeated factors.

2 x 2 x 2 x 3 x 3 x 3 = 216

23 x 33 = 216

Answer 8

The exponent is just a way to keep track of repeated factors.

The prime factorization of 72 is 2 x 2 x 2 x 3 x 3

With exponents, that's 2^3 x 3^2

Answer 9

22 x 52 = 100