CHAPTER 1: - INDICES AND LOGARITHMS(JSS3 AND SS1)
LAWS OF INDICES(PART 1)
The following laws of indices are true for all values of n, I and x ≠0.
1. xn × x? = xn??
2. xn ÷ x? = xn??
3. x° = 1, x ≠0
4. x-n = 
5. (xn)? = xn?
6. x
= 
7. x
= 
or (
)n
EXAMPLE 1
Simplify
a. 102 × 10³
b. 22n7 ÷ 2n³
c. 19°
d. 5?2
e. 2³ × (
)?¹
f. r × r° × r?5.
a) 102 × 10³ = (10 × 10) × (10 × 10 × 10)
= 10 × 10 × 10 × 10 × 10
= 105
Check: 102 × 103 = 102+3 = 105 (Law 1)
b) 22n7 ÷ 2n3 = 
× n7-3 = 11n4 (Law 2)
Check:
22n7 ÷ 2n3
= 
= 11 × n × n × n × n = 11 × n4
= 11n4
a) 190 = 1 (Law 3)
Check:
190 = 19n-n (since n – n = 0)
= 
(Law 2)
= 1 (num. and denom. are equal)
b) 5?2 = 
= 
(Law 4)
Check:
5?2 = 5°?²
= 
(Law 2)
= (Law 3)
=
c) 23 × () ?¹ = 8 × 
(Law 4)
= 8 × 6 = 48
d) r × r° × r?5 = r1?°?(?5) (Law 1)
= r?4 = 
or r × r° × r?5 = r1 × 1 × 
(Laws 3
= and 4)
EMAIL: ebuleprecio@gmail.com
AUTHOR: EBULE PRECIOUS ORITSEMEYIWA
LOCATION: WARRI, DELTA STATE
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