A number *raised to a power* is the number of times a number is multiplied by itself: 5^{4} is 5 *raised to the power* of 4 and is equivalent to 5 x 5 x 5 x 5 = 625.

The small number, the **index**, indicates how many times the number appears when being multiplied by itself:

2^{5} means 2 x 2 x 2 x 2 x 2

The 2 appears 5 times.

Similarly, the root of a number can be other than 2 or 3 (square root or cube root). Other roots can be used: `root(4)` (a small 4 on top of a square root sign) is the fourth root of a number.

For example, `root(4)1296` = 6, as 6 x 6 x 6 x 6 = 1296.

10^{3 is 10 x 10 x 10 = 1000, or one thousand.}

106 is 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000, or one million.

*To calculate a power or root for any given number, make sure you understand how to do it on your calculator. Each type of calculator has a different way of entering the calculation.*

What is (`frac(2)(3)`)^{4}?

Multiply four of the fractions together: `frac(2)(3)` x `frac(2)(3)` x `frac(2)(3)` x `frac(2)(3)`

Answer: `frac(16)(81)`

What is `root(4)0.0081`?

0.3 x 0.3 x 0.3 x 0.3 = 0.0081 Check the number of decimal places involved by calculating the inverse operation.

Answer: 0.3

See also Terms with Powers and Calculating with Indices

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