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.
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.
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.
2 x 2 x 2 x 3 x 3 x 3 = 216
23 x 33 = 216
No prime power exists since there are no duplicate prime numbers in the prime factorization.
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.
Exponents are just shorthand for repeated factors.
2 x 2 x 2 x 3 x 3 x 3 = 216
23 x 33 = 216
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
22 x 52 = 100
No prime power exists since there are no duplicate prime numbers in the prime factorization.
3 x 5^2 = 75
3 x 5 x b = 15b No exponents required.
24=2*12=2*2*6=2*2*2*323*3
Prime Factorization of 9 is 3x3=9 So it is 3 to the second power
The prime factorization of 81 using exponents is: 34
The prime factorization of 600 using exponents is: 23 x 3 x 52
The prime factorization of 540 using exponents is: 22 x 33 x 5
The prime factorization of one billion using exponents is 2^9 x 5^9
32 = 25
245 = 5x72
No prime power exists since there are no duplicate prime numbers in the prime factorization.
The prime factorization of 252 using exponents is: 22 x 32 x 7
2 x 3 = 6 No exponents needed.
3 x 5 = 15 No exponents required.
36 = 22*32.
24 = 23 × 3