Integer Powers and Roots

Integer Powers and Roots

GCSE(F) GCSE(H)

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

Examples

1. What is (`frac(2)(3)`)4?

Answer: `frac(16)(81)`

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

2. What is `root(4)0.0081`?

Answer: 0.3

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.