There are some laws are given below –
1) aᵐ X aⁿ = aᵐ⁺ⁿ and aᵐ X aⁿ X aᵖ = aᵐ⁺ⁿ⁺ᵖ
2) aᵐ ÷ aⁿ = aᵐ X a⁻ⁿ = aᵐ⁻ⁿ
3) (a X b)ᵐ = aᵐ X bᵐ or (a X b)ⁿ = aⁿ X bⁿ
4) (aᵐ)ⁿ = aᵐⁿ
5) aᵐ = aⁿ = 1 ( if m = n = 0 and a ≠ 0 )
6) aᵐ = aⁿ = a ( if m = n = 1 and a ≠ 0 )
7) If aᵐ = aⁿ ( when m = n and a ≠ 0 )
a aᵐ
8) ( -------- )ᵐ = ----------
b bᵐ
9) [{(a)ᵐ}ⁿ]ᵖ = [{aᵐ}ⁿ]ᵖ = [aᵐⁿ]ᵖ = aᵐⁿᵖ
10) If n is an even integers, (-1)ⁿ = (-1)²ᵐ = {(-1)²}ᵐ = {(-1) X (-1)}ᵐ = 1ᵐ = 1
11) If n is an odd integers, (-1)ⁿ = (-1)²ᵐ⁺¹ = (-1) X (-1)²ᵐ = (-1) X (1) = -1
12) n√a = a¹∕ⁿ
13) aᵐ∕ⁿ = (aᵐ)¹∕ⁿ
14) a¹∕ᵐ¹∕ⁿ = a¹∕ᵐⁿ