# Powers And Roots

Powers can be defined as process of multiplying a number itself multiple number of times. Powers are also called as indices.

Suppose 2n in this example n = power, index. If we put n = 2, that means we want to calculate 22 = 4. 22 means we have to multiply 2 and 2, means 22 = 2 * 2= 4. Here 'n' tells us number of 2's to be multiplied together. So when we wish to multiply a number by itself we use power.

For example: 3 * 3 * 3 * 3* 3 * 3 is written as 36. Hear 6 is called power or index and 3 is called base.

So 3 * 3 * 3 *3 * 3 * 3 = 36 . If base of any two numbers is same then there powers will be added. To understand this concept let us take an example : 23 and 24 in this case base is same which is 2 and power is 3 and 4 respectively. So, 23 * 24 = 2 (3+4) = 27.

Example = 7 * 7, we can say that 7 raised to power 2 is 49.
Reverse process of powers is called root. Square root means number raised to power half. Suppose we want to find the square root of (k) ½ n------ equation 1. Here 'k' is base. In this equation if we put n = 2 , and k = 4 then it will become square root, root of 4 is 2, we can write this equation as (2*2)1/2 => (4)1/2 = 2, this is called square root.

Cubic root can be represented by power of 1/3 raised to a number. Lets take an example of cubic root (27)1/3. We can write 27= 3 * 3 * 3, so (27)1/3 = 3 , this is called cube root.

We will take an example of powers and roots:

Root of 25 is = 5 and square is 625 so power and roots of 25 is respectively 5 and 625.

If we want to calculate 36 power roots it means (36)1/2 = 6.