(i) a^m.aⁿ= a^m+n

eg . 2².2³= 2²⁺³= 2⁵= 32

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(ii) a^m ÷ aⁿ = a^m x 1/aⁿ = a^m. a^-n= a^m-n

eg. (a) 2³÷ 2²= 2^3-2= 2¹= 2

(b) 2²÷ 2³= 2^2-3 = 2^-1= 1/2

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(iii) (a^m)ⁿ= a^mn

(2²)³= 2⁶

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(iv) a^-n = 1/aⁿ

eg. 2^-3= 1/2³

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(v) a^m/n= (a^m)^1/n= (a^1/n) ^m

eg. (2)^3/2= (2³)^1/2= (2^1/2)³

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(vi) (ab)^m = a^m.b^m

eg . (2.3)³= 2³.3³

(6)³= 8x 27

216 = 216

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(vii) (a/b)^m= a^m/b^m

eg . (2/3)²= 2²/3²

4/9 = 4/9