Powers can be defined as process of multiplying a number itself multiple number of times. Powers are also called as indices.
Suppose 2^{n} in this example n = power, index. If we put n = 2, that means we want to calculate 2^{2} = 4. 2^{2} means we have to multiply 2 and 2, means 2^{2} = 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 3^{6}. Hear 6 is called power or index and 3 is called base.
So 3 * 3 * 3 *3 * 3 * 3 = 3^{6} . If base of any two numbers is same then there powers will be added. To understand this concept let us take an example : 2^{3} and 2^{4} in this case base is same which is 2 and power is 3 and 4 respectively. So, 2^{3} * 2^{4} = 2 ^{(3+4) }= 2^{7}.
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.
Roots and Radicals are actually similar terms you can call roots as radicals also. Radicals and roots are inverse operation to exponential operation. When we square 5, then it will get 25 but when we find square root of 25, it will give 5. When we square 4, we get 16 and square root of 16 will give 4. Square root is symbolized by '√' sign. Actually square r...Read More
Exponents and radicals are very frequently used expressions in algebraic operations. Exponent represents the number of times a number should be multiplied to itself. For instance, (Y – 4) ^{2} means multiplying (Y – 4) twice. Radicals are those quantities which are found in roots of some random degrees. For example, symbol for root w...Read More
Rational exponents can be defined as alternate way to represent roots. It is easy to write radicals in form of rational exponents and can be solved by using the laws of exponents. Rational exponents are also called as fractional exponents. Expression y^{(a/b)} is representing rational exponent. The denominator of rational exponent becomes the i...Read More