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
To write ( bxbxbxbxbxb ) in short index form, you can group the terms. Since there are six ( b )s multiplied together, you can express it as ( b^6 ). Therefore, the short index form of ( bxbxbxbxbxb ) is ( b^6 ).
2^2 x 3 x 5
360= 23 times 45
23 x 33 = 216
5x4x2x4x3x5x5x4
2^2 x 3 x 5 = 60
840 = 23 x 3 x 5 x 7
Index form of 9765625 is 9.765625 × 106
Oh honey, let me break it down for you. 160 can be expressed as 2^5 * 5^1. In index form, that would be written as 2^5 * 5. So there you have it, 160 expressed as a product of prime numbers in index form. Hope that clears things up for ya!
Prime factors of 1080 are 23 33 5.
This is the prime factorization of 80 in index form: 80 = 2 x 2 x 2 x 2 x 5 = 24 x 5
2^4 x 3 x 5
2^2 x 3 x 5
Writing 144 in index form involves expressing it as a base raised to a certain power. In this case, 144 can be written as 12^2, where 12 is the base and 2 is the power to which it is raised. This is because 12 multiplied by itself (12^2) equals 144.