To write a number in index form, you find its prime factors, then write the result as the product of powers of primes - that's a mouthfull!
e.g. 360 = 2*180 = 2*2*90 = 2*2*2*45 = 2*2*2*3*15 = 2*2*2*3*3*5 = 23*32*5 See related link for more explanation and examples.
360= 23 times 45
23 x 33 = 216
Writing Numbers in Index FormWe know that: So, we can write 8 as 23.Likewise, 27 can be written as 33and 125 can be written as 53.So far, we have considered numbers that have a group of the same factors. Sometimes, a number has more than one group of the same factors as shown in the following example.Example 20Write 200 in simplest index form.Solution:Key Termsimplest index form
2^2 x 3 x 5
Prime numbers don't factorize; they're already prime.
360= 23 times 45
23 x 33 = 216
5x4x2x4x3x5x5x4
2^2 x 3 x 5 = 60
840 = 23 x 3 x 5 x 7
It is: 2^5 times 5^1 = 160
Index form of 9765625 is 9.765625 × 106
Prime factors of 1080 are 23 33 5.
360 = 2 x 2 x 2 x 3 x 3 x 5 = 23 x 32 x 5
2^4 x 3 x 5
It is: 2^4 times 3^2 = 144
2^2 x 3 x 5