Laws Of Exponent With Examples

 

Introduction:

Consider a number Zn .Zn reads as the nth power of Z. Or Z raised to the power n. Here Z is base whereas n is exponent, power, or order. Or simply exponent is repeated multiplication. 

Law 1: Multiplication of two terms with identical bases:

To multiply two numbers having identical bases, simply add the exponents whereas base remains the same.


Zm.Zn = Zm+n


Examples:


23.26 = 29

Law 2: Multiplication of two terms with identical exponents:

To multiply two numbers  having identical exponents but different bases, multiply the bases whereas exponent remains the same. We can write them as follows. Let's do some examples.


Zm.Ym =  (Z.Y)m


Examples:


23.33 = (2*3)3


Law 3: Division of two terms with identical bases:

To divide two numbers having identical bases, subtract the powers whereas the base remains the same.


Zm/Zn = Zm-n


Examples:


55/53 = (5)5-3

Law 4: Division of two terms with different bases and identical exponent:


To divide two numbers having identical exponents but different bases, we can write them as follows.  


Zm/Ym = (Z/Y)m

Law 5: A term with two or more exponents (power of power):


When two or more exponents are there, or one power raised to another power, then simply multiply the exponents whereas base remains the same.


(Zm)n = Zm*n


Examples:

(32)3 = 32 x 32 x 32 = 32+2+2 = 36

(32)3 = 32*3 = 36

Law 6: Base with exponent is 1

Whenever exponent is 1, base remains the same.


Z1 = Z


Examples:

21 = 2

31 = 3

Law 7: Base with exponent is 0

Whenever exponent is 0, the answer will be 1.


Z0 = 1


Examples:

  1. 30 = 1


  1. (31/31) = 31-1 = 0

Law 8: negative exponent:


Numbers with positive exponents means repeated multiplication whereas numbers with negative exponents means repeated division. Let's do some examples.


Z-m = 1/Zm


Examples:


Z-2 = 1/Z2


Test:

  1. 25.35 = 55

  2. 3x2 . 2x3 

= (3.2)*(x2+3)

  1. 3.x.y.x2.y3.5

= (3.5)(x.x2)(y.y3)

= 15 x3.y4

  1. (x-9.y4.z-1) ÷ (x-7.y2.z-4)

           = x-9+7 . y4-2 . z-1+4

           = x-2 . y2 . z3

  1. 52.(53)2 ÷ 52

= 52. 56 ÷ 52

= 52. 56-2

= 52. 54

= 52-4

= (⅕)2

  1. (5/15)-2

= (⅓)-2

= 32




Laws of exponent explanation & examples for beginners
Location: Solomon Islands

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