In this chapter we are going to solve some examples based on division of terms with same exponents for example (2/5)^{3}.

In the example (2/5)^{3} can be written as (2/5) x (2/5) x (2/5),

again it can be written as (2 x 2 x 2)/(5 x 5 x 5) = 2^{3}/5^{3}.

Therefore we get the result for (2/5)^{3} as 2^{3}/5^{3}.

Let us discuss few more examples :

•(5/7)^{3}

•(8/3)^{4}

•(X/Y)^{11}

In the first example, i.e., (5/7)^{3}.

Which can be written as (5/7) x (5/7) x (5/7) = (5 x 5 x 5)/(7 x 7 x 7) = 5^{3}/7^{3}.

Therefore the result for (5/7)^{3} = 5^{3}/7^{3}.

Coming to second example, i.e., (8/3)^{4}.

Which can be written as (8/3) x (8/3) x (8/3) x (8/3) = (8 x 8 x 8 x 8)/(3 x 3 x 3 x 3) = 8^{3}/3^{3}

Therefore the result for (8/3)^{3} = 8^{3}/3^{3} .

In the last example, i.e., (X/Y)^{11}.

Which can be written as (X/Y) x (X/Y) x (X/Y) x (X/Y) x (X/Y) x (X/Y) x (X/Y) x (X/Y) x (X/Y) x

(X/Y) x (X/Y) = (X x X x X x X x X x X x X x X x X x X x X)/(Y x Y x Y x Y x Y x Y x Y x Y x Y x Y x Y) = X^{3}/Y^{3}.

Therefore the result for (X/Y)^{11} = X^{11}/Y^{11}.

The examples have been illustrated in the video below :