Integer Powers and Roots

## Integer Powers and Roots

A number raised to a power is the number of times a number is multiplied by itself: 54 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:

25 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.

103 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.

## Example 1

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)

## Example 2

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.