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.
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