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Zero Exponents

 
 

As we have already learnt the concept of exponent which is a shorthand notation. Let us learn about zero exponent which means for any non zero integer a0 is 1.

 

Let us try to solve few  examples :

  • 31

  • 25

 

In the first example 31. Here 3 is multiplied itself for 1 time we get as 3.

Therefore for 31 we get the result as 3

 

Coming to second example 25. Here 2 is multiplied itself for 5 times,
i.e., 2 x 2 x 2 x 2 x 2 we get as 32.

 

Therefore for 25 we get the result as 32.

Let us try to solve few more examples by the two patterns below :

 

     Exponents

     Values

     Exponents

      Values

      24

       = 16

      34

      = 81

      23

       =  8

      33

      = 27

      22

       =  4

      32

      = 9

      21

       =  2

      31

      = 3

      20

       =  ?

      30

      = ?

 

In the above table the exponents, i.e., 24,23,22,21,20 are decreasing by power 1, whereas the values, i.e., 16,8,4,2 are decreasing by half.
Let us follow it and solve the value of 20, here half of 2 is 1.

 

Therefore we get the result for 20 as 1.

 

Coming to other exponents, i.e., 34,33,32,31,30 are decreasing by power 1, whereas the values, i.e., 81,27,9,3  are decreasing by one-third.
Let us try to follow it and solve the value of 30, here half of 3 is 1.

 

Therefore we get the result for 30 as 1.

 

Similarly we can say

40=1, 50=1, 60=1 and so on….

 

Thus for any non zero integer a, we get  a0 = 1.

 

The examples have been illustrated in the video below :

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