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Exponential Terms With Negative Base Example -1

Already we have learnt the concept of negative base and now let us proceed with the examples.

  • 81/16

Here 81 can be written as 3 x 3 x 3 x 3 = 34

        16 can be written as 2 x 2 x 2 x 2  = 24

         we can write 81/16 as 34/24

                  34/24 = (3)4/(2)4 =(3/2)4

Therefore we get result for 81/16 as (3/2)4.

 

  • 25/64

Now 25 can be written as 5 x 5,

        64 can be written as 8 x 8.

       We can write 25/64 as 52/82

          25/64 = 52/82 = (5/8)2

Therefore we get the result for 25/64 as (5/8)2.

Let us try to solve few more examples :

 

  1. -27/125

  2. -243/32

 

In the first example  -27/125, here -27 = (-3) x (-3) x (-3) = (-3)3

                                                        125 = 5 x 5 x 5 = (5)3

                                                 -27/125 = (-3)3/(5)3 = (3/5)3.

 

Therefore we get the result for -27/125 as (3/5)3.

 

Coming to second example -243/32, here -243 = (-3) x (-3) x (-3) x (-3) x (-3) = (-3)5

                                                                           32 = (2) x (2) x (2) x (2) x (2) = (2)5

                                                                  -243/32 = (-3)5/(2)5 = (-3/2)5

 

Therefore we get the result for -243/32 as (-3/2)5.

In the above examples am/bm = (a/b)m property has used.

 

The examples have been illustrated in the video below :

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