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Laws of Exponents - Dividing Powers with the Same Base

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formula

For any non-zero integer a, where m and n are whole numbers and m > n, am ÷ an = am – n.

notes

Dividing Powers with the Same Base:

In general, for any non-zero integer a, am ÷ an =am – n, where m and n are whole numbers and m > n.

Consider the following examples,

(i) 79 ÷ 76

= `7^9/7^6`

= `(7 × 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7)/(7 × 7 × 7 × 7 × 7 × 7)`

= 7 × 7 × 7 = 73 = 79 - 6................(am ÷ an = am−n)

(Note, in 79 and 76 the base is same and 79 ÷ 76 becomes 79 - 6.)

(ii) a8 ÷ a5

= `a^8/a^5`

= `(a × a × a × a × a × a × a × a)/(a × a × a × a × a)`

= a × a × a = a3 = a8-5...................(am ÷ an = am−n)

(iii) 8t ÷ 82 

= `(8^t)/(8^2)`

= 8(t − 2)....................(am ÷ an = am−n)

Example

Solve: (- 2)5 ÷ (- 2)3

(- 2)5 ÷ (- 2)3

`(- 2)^5/(- 2)^3`

`= ((- 2) xx (- 2) xx (- 2) xx (- 2) xx (- 2))/((- 2) xx (- 2) xx (- 2))`

= (- 2)2

(- 2)5 ÷ (- 2)= (- 2)2.

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