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 :

- 4
^{6}/ 4^{2} - 8
^{2}/ 8^{7}

In the first example, i.e., 4^{6} / 4^{2} 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 4^{4}.

Therefore we get the result for 4^{6} / 4^{2} as 4^{4}.

Coming to second example, i.e., 8^{2} / 8^{7} 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 1/8^{5} or 8^{-5}.

Therefore we get the result for 8^{2} / 8^{7} as 8^{-5}.

Let us try to solve few more examples :

- 7
^{5}/ 7^{3}. - 5
^{3}/ 5^{5}.

In the example 7^{5} / 7^{3} = (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 7^{2}. In short 7^{5} / 7^{3} = 7^{5-3} = 7^{2}.

Therefore the result for 7^{5} / 7^{3} = 7^{5-3}

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

Therefore the result for 5^{3}/5^{5} = 1/5^{5-3}

The examples are been illustrated in the video below :