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Laws of Exponents - Dividing Powers with Different Base and Same Exponents

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Topics

formula

am ÷ bm = `a^m/b^m = (a/b)^m`, where a, and b are any non-zero integers and m is a whole number.

notes

Dividing Powers with the Same Exponents:

If we have to divide the powers where the base is different but exponents are the same then we will divide the base.

am ÷ bm = `a^m/b^m = (a/b)^m`, where a, and b are any non-zero integers and m is a whole number.

(i) `(2^4)/(3^4)`

= `(2 xx 2 xx 2xx 2)/(3 xx 3 xx 3 xx 3)`

= `2/3 xx 2/3 xx 2/3 xx 2/3`

= `(2/4)^4`

(ii) `(a^3)/(b^3)`

= `(a xx a xx a)/(b xx b xx b)`

= `a/b xx a/b xx a/b`

= `(a/b)^3`.

Example

Expand: `(3/5)^4`

`(3/5)^4 = 3^4/5^4 = (3 xx 3 xx 3 xx 3)/(5 xx 5 xx 5 xx 5).`

Example

Expand: `((-4)/7)^5`

`((-4)/7)^5 = (-4)^5/7^5 = ((-4) xx (-4) xx (-4) xx (-4) xx (-4))/(7 xx 7 xx 7 xx 7 xx 7)`

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