SS1 First Term Further Mathematics Lesson Note – Laws of Indices

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WEEK ONE

LAWS OF INDICES:

CONTENT:

1. Laws of Indices
2. Application of Indices Linear Equations
3. Application of Quadratic Equations

LAWS OF INDICES

There are laws governing the use of indices. These are useful in other subjects. They are;

1. aⁿ x a^m = a^n+m

Therefore

a³ x a³  = a x a x a x a x a x a = a⁶                 i.e  a³⁺³   = a⁶

In general, when multiplying indices with same base, you add the power

 

2. aⁿ ÷ a^m = a^n-m .

a⁵ ÷ a⁴ = a^5-4 = a¹

Also, a⁵ ÷ a⁴ =  = a

In general, when dividing indices with the same base, you subtract the power

 

3. (aⁿ)^m= a^n×m = a^mn

(a³)² = a^3×2 = a⁶ 

 

4. a⁰ =1

a⁵ ÷ a⁵ = a^5-5 = a⁰

Also, a⁵ ÷ a⁵ =  = 1

This implies that anything to power zero is equal to 1, i. e  5⁰ = 1, 2⁰ = 1

 

5. a^-n= 1/aⁿ

Consider a⁵ ÷ a⁶ = a^5-6 = a^-1

But a⁵÷ a⁶ =  =

a^-1 =

In the same way  a^-2= ,

6. a ^n/m = ⁿ = )

Consider (8) ^1/3 = (2³) ^1/3 = (2³) ^1/3 = 2

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