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Division Of Terms With Same Exponents

We are going to learn in this chapter a new concept, i.e., dividing a term by another term with same exponent.Let us solve the examples :
 

  1. (8/3)3
  2. (5/7)4

 
In the first example, i.e., (8/3)3 can be written as (8/3) x (8/3) x (8/3), again can be written as
(8 x 8 x 8) / (3 x 3 x 3), according to the law can be written as 83 / 33.
 
Therefore we get the result for (8/3)3 as 83 / 33.
 
Coming to second example, i.e., (5/7)4 can be written as (5/7) x (5/7) x (5/7) x (5/7), again can be written as (5 x 5 x 5 x 5) / (7 x 7 x 7 x 7), according to the law can be written as 54 / 74.
 
Therefore we get the result for (5/7)4 as 54 / 74.
 
Let us try to solve few more examples :
 

  • (7/4)5
  • (a/b)m
  • (5/7)3

In the first example, ie., (7/4)5 = (7/4) x (7/4) x (7/4) x (7/4) x (7/4)

                                               = (7 x 7 x 7 x 7 x 7) / (4 x 4 x 4 x 4 x 4)

                                               = 75 / 45.

 

Therefore the result for (7/4)5 = 75 / 45.

 

Coming to second example, i.e., (a/b)m = (a/b) x (a/b) x …. m times

                                                            = (a x a x … m times) / (b x b x … m times) times

                                                             = am / bm.

 

Therefore the result for (a/b)m = am / bm.

 

In the last example, i.e., (5/7)3 = (5/7) x (5/7) x (5/7)

                                               = (5 x 5 x 5) / (7 x 7 x 7)

                                               = 53 / 73

Therefore the result for (5/7)3 = 53 / 73.

       In the examples, (a/b)m = am/bm concept is used.

 

The examples are been illustrated in the video below :

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