What does it mean with a number and a small number just to the right top?

Answer 1

I guess you mean something like 2³ (also written as 2^3)

Here the little number to the top right is the index or power and it tells you how many times the number is multiplied by itself; with 2³ it means that the 2 is multiplied by itself 3 times, ie 2³ = 2 × 2 × 2 = 8.

There are various rules to how to handle the indices.

* If a number with two different indices are multiplied together, the indices are added, eg 2^3 × 2^5 = 2^(3+5) = 2^8

* If a number with two different indices are divided, the indices are subtracted, eg 2^8 ÷ 2^5 = 2^(8-5) = 2^3

* If the index is 1, the result is the number, eg 2^1 = 2

* If the index is 0, the result is 1 regardless of the number, eg 2^0 = 5^0 = 10^0 = 1

* if a number with an index is again indexed, the indices are multiplied together, eg (2^3)^5 = 2^(3×5) = 2^15

The power can also be negative, as in 2^-3. This is the same as the reciprocal of 2^3, ie 2^-3 = 1/2³ = 1/8

The power does not have to be a whole number. eg 16^½. Using the above rules, (16^½)^2 = 16^(½×2) = 16^1 = 16. But any number to the power 2 is that number squared, so (16^½)^2 is 16^½ squared, but this is 16, meaning that 16^½ is the square root of 16, ie the power of ½ takes the square root of the number: 16^½ = √16 = 4.

Answer 2

It is called an index but can also be called power or exponent. This browser does not support superscripts and so, like with spreadsheets, the raised number, n, is written as "^n".

In its simplest form, where n is a positive integer, the expression x^n represents n lots of x multiplied together. Many people incorrectly say that it is x multiplied by itself n times: it is NOT!

Thus, for example, 7^3 = 7*7*7

Seven multiplied by itself 3 times would be 7*7(once)*7(two times)*7(three times) - one too many sevens.

There are special laws for dealing with indices and these enable mathematicians to make sense of indices that are negative, rational, real or even complex numbers.