The 8 Exponential Rules of Algebra

Algebra is one of the commonest topic in Mathematics, making it essentially indispensable for every student of Mathematics.

Below are 8 of its exponential rules every beginner must know:

Rule 1:    a^m x aⁿ = a^m+n

Example:

3² x 3³ = 3²⁺³ = 3⁵

Rule 2:  (aⁿ)^m  =  a^nm

Example:

(5²)³  =  5^2x3 = 5⁶

Rule 3:  (ab)ⁿ  = aⁿ x bⁿ

Example:

(4x6)² = 4² x 6²

Rule 4:  a^-n = 1/aⁿ 

Example:

8^-3 = 1/8³ 

Rule 5:  (a/b)^-n = (b/a)ⁿ

Example:

(6/5)^-2 = (5/6)²  

Rule 6:  (a/b)ⁿ = aⁿ/bⁿ 

Example:

(9/3)² = 9²/3² 

Rule 7:  aⁿ/a^m = a^n-m 

Example:

12⁵/12³ = 12^5-3

Rule 8:  a⁰ = 1 

Example:

7⁰ = 1  (Every other number raised to the power of zero equals one).

Practical exercises

Solve the following:

a.     16 x  4^-2 

b.     (10³)⁴ 

c.      (9/18)^-3

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