5.1 Indices and Laws of Indices (Part 1)


Positive Integral Indices
When a real number a is multiplied by itself n times, the result is the nth power of a.

Example:  5×5×5×5 = 5(5 to the power of 4)

In general, if a is any real number and n is a positive integer, then


The integer n is called the index or exponent and a is the base.


5.1 Indices and Laws of Indices (Part 1)
(A) Zero Indices
The zero index of any number is equal to one.

  a 0 = 1, where a ≠ 0

Example 1:
Find the value of the followings:
(a) 2500
(b)0.5130
(c)  ( 2 7 ) 0 (d)  ( 11 1 25 ) 0

Solution:
(a) 2500 = 1
(b)0.5130 = 1
(c)  ( 2 7 ) 0 = 1 (d)  ( 11 1 25 ) 0 = 1


(B) Negative Integral Indices

   a n  is a reprocal of  a n .       a n = 1 a n

Example 2:
Find the value of the followings:
(a) 102 -1
(b)  –6 -3
(c)  ( 1 3 ) 4 (d)  ( 2 5 ) 2 (e)  ( 2 5 ) 4

Solution:
(a)  102 1 = 1 102 (b)  6 3 = 1 6 3 = 1 216 (c)  ( 1 3 ) 4 = ( 3 ) 4 = 81 (d)  ( 2 5 ) 2 = ( 5 2 ) 2 = 25 4 (e)  ( 2 5 ) 4 = ( 5 2 ) 4 = 625 16

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