Form 2 Unit 1 Lesson 2- Index Notations

Objective

At the end of the lesson, students should be able to:

• Use the index notation with any given numerical base/bases.

Index notation is used to show when a number is being multiplied by itself. The base shows the factor that is repeated and the index/exponent/power represents the number of times the multiplication occurs.

Example 1

Write the following in index form

1. 2 × 2 × 2 × 2 × 2 6 ×7 × 6 × 7 × 6 ×7        c. 3 × 3 × 4 × 4 × 4

Solution

a) 2 × 2 × 2 × 2 × 2

Since the factor in question (a) is 2, 2 is the base. It is repeated 5 times therefore the power/exponent/index is 5.

Therefore 2 × 2 × 2 × 2 × 2 =2⁵

b) 6 × 7 × 6 × 7 × 6 × 7

In this question, we have two different bases; 6 and 7. 6 is repeated 3 times and 7 is repeated 3 times

Therefore 6 × 7× 6 × 7 × 6 × 7=6³ ×7³

c) 3 × 3 × 4 × 4 × 4

We have two bases 3 and 4. 3 is repeated twice hence its index/ power/exponent is 2. 4 is repeated thrice hence its index/power/exponent is 3.

Therefore 3 × 3 × 4 × 4 × 4 × 4 = 3²  × 4³

Example 2

Write in expanded form

a) 3⁴                    b) 2⁴ ×3³                         c)  (2 × 9)²

Solution

a) 3⁴ = 3 x 3 × 3 × 3

b) 2⁴× 3³=2 × 2 × 2 × 2 × 3 × 3 × 3

c) (2 × 9)²

The exponent 2 outside the bracket indicates that everything in the bracket is multiplied twice.

(2×9) × (2×9) =2 × 9 ×2 × 9= 2 × 2 × 9 × 9