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Negative Exponents

Negative exponents means the power(exponent) of a number is negative(-).If a number in numerator

having negative exponent is to be reciprocal by positive (i.e., a-m = 1/am)

 

Let us try to solve few examples :

 

  • 2-3

In the example 2-3, here exponent is negative i.e., -3 and we know that 23 can be written as 2 x 2 x 2 we get 8. Now we can write 2-3 as 1/23 = 1/8

 

Therefore we get the result for 2-3 as 1/23

 

  • 3-6

In this example 3-6, here exponent is having negative number i.e., -6 and we know that 36 can be written as 3 x 3 x 3 x 3 x 3 x 3, we get 729. Now we can write 3-6 as 1/36 = 1/729.

 

Therefore we get the result for 3-6 as 1/36.

 

Let us try to solve few more examples :

 

         Exponents

  Values

     Exponents

            Values

         24

     =16

        34

       = 81

         23

     =8

33

    = 27

         22

    =4

32

    = 9

         21

     =2

31

    = 3

         20

      =1

30

    = 1

         2-1

         = ?

3-1

    = ?

          2-2

      = ?

3-2

   = ?

 

In the above table the exponents, i.e., 24,23,22,21,20,2-1,2-2 are decreasing by 1, whereas values, i.e., 16,8,4,2,1 are decreasing by half. Following the same we get values of 2-1 and 2-2.

By negative exponent 2-1 = 1/2

Now 2-2 = 1/22 = 1/4

Coming to third column, the exponents, i.e., 34,33,33,32,31,30,3-1<.sup>,3-2 are decreasing by 1, whereas values, i.e., 81,27,9,3,1 are decreasing by one-third. Following the same we get values of 3-1 and 3-2.

By negative exponent 3-1 = 1/3

and now 3-2 = 1/32 = 1/9

In the examples a-n = 1/an property is used.

 

The examples have been illustrated in the video below :

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