Rules of Exponent

Hi, In this post we will discuss about the rules of exponent which will help in calculation.

Formulas and properties of exponents are used in the reduction and simplification of expressions, and in solving equations and inequalities.

Rules of exponent:

Rule 1.  a⁰ = 1

             Ex :  2⁰ = 1  ,   (23)⁰ = 1  ,   (342)⁰ = 1

Rule 2.  (aⁿ)^m = a^nm

             Ex:  (2²)³ = 2^{2 x 3} = 2⁶

Rule 3. aⁿ  ×  a^m = a^n + m

             Ex:  4³  ×  4⁵ = 4^3 + 5 = 4⁸

Rule 4. aⁿ  ÷ a^m = a^{n - m}

             Ex:  3⁷  ÷  3⁴ = 3^7 - 4 = 3³

Rule 5.  aⁿ  =  a^m   =>  n = m

Rule 6.  a^m  =  b^m   =>  a = b

Practice Questions :

1.     7⁰ =?  ,   (876)⁰ =?

2.     6⁵  ×  6² = ?

3.     5⁷  ÷  5³ = ?

4.     (4³)⁴ =?

5.     Find the value of ‘x’.

                               i.            4^{2 +  x} = 4⁵  [hint: Use rule no. 5]

                             ii.            (x - 4)³ = 8³   [hint: Use rule no. 6]


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