# 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

Solution:
(a) 2500 = 1
(b) 0.5130 = 1

(B) Negative Integral Indices

Example 2:
Find the value of the followings:
(a) 102 -1
(b)  –6 -3

Solution: