Laws of Exponents - Dividing Powers with the Same Base

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

Dividing Powers with the Same Base:

In general, for any non-zero integer a, a^m ÷ aⁿ =a^{m – 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 = 7^{9 - 6}................(a^m ÷ aⁿ = a^m−n)

(Note, in 7⁹ and 7⁶ the base is same and 7⁹ ÷ 7⁶ becomes 7^{9 - 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 = a^8-5...................(a^m ÷ aⁿ = a^m−n)

(iii) 8^t ÷ 8² 

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

= 8^{(t − 2)}....................(a^m ÷ aⁿ = a^m−n)