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

#### 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.

# 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)

If you would like to contribute notes or other learning material, please submit them using the button below.

### Shaalaa.com

Dividing Powers With the Same Exponents [00:04:21]
S
0%