Earlier we saw that 15288 = 2 x 2 x 2 x 3 x 7 x 7 x 13. It is possible to write the product in a shorter way. 23 is a short way of writing 2 x 2 x 2. The number 3 in 23 is called the index or power. It shows that three 2's are to be multiplied together. In the same way, 72 is a short way of writing 7 x 7. The index 2 shows that two 7's are to be multiplied together.
In index form, 15288 = 23 x 3 x 72 x 13. The use of index form saves space and can help to prevent errors in counting and copying. It would be easy to make a mistake when copying the product of factors of 256.
2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
In index form, 256 = 28².
This saves space and clearly shows that eight 2's are to be multiplied together.
We say 28 as 'two to the power of eight', or 'two to the eighth power' or 'two raised to the power of eight' or, often, just 'two to the eighth'. The plural of index is indices. The indices 2 and 3 are usually said in a special way: 7² as 'seven squared', 2³ as 'two cubed'.
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