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Division Of Exponents Having The Same Base

We know that exponents are shorthand notation. Now moving to a new concept, i.e., dividing a exponent(power) by another exponent with the same base. Let us try to solve few examples :

  1. 46 / 42
  2. 82 / 87

In the first example, i.e., 46 / 42 can be written as (4 x 4 x 4 x 4 x 4 x 4) / (4 x 4).
Here cancel the numerator and denominator 4, which are repeated then we get (4 x 4 x 4 x 4) written as 44.

Therefore we get the result for 46 / 42 as 44.

Coming to second example, i.e., 82 / 87 can be written as (8 x 8/ 8 x 8 x 8 x 8 x 8 x 8 x 8) by cancelling the repeated values we get 1/85 or 8-5.

Therefore we get the result for 82 / 87 as 8-5.

Let us try to solve few more examples :

  • 75 / 73.
  • 53 / 55.

In the example 75 / 73 = (7 x 7 x 7 x 7 x 7/ 7 x 7 x 7) by cancelling only (7 x 7) remains which can be written as 72. In short 75 / 73 = 75-3 = 72.

Therefore the result for 75 / 73 = 75-3

In the last example, i.e., 53 / 55 = (5 x 5 x 5/ 5 x 5 x 5 x 5 x 5) = 1/55-3 = 1/5< sup>2 or 5-2

Therefore the result for 53/55 = 1/55-3

The examples are been illustrated in the video below :

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