Form 2 Unit 1 Lesson 3 – First and Second laws of Indices

Objective

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

  • Use the first and second index laws or laws of indices.

First law of indices:

When multiplying numbers in the index form, if the bases are the same, the powers are added.

Second law of indices:

When dividing numbers in index form, if the bases are the same, the powers are subtracted.

 

Example 1

Write the expanded form of the following then simplify:

a. 33× 34             b. 22 ×22×32

 

Solution

a. 33× 34

=3×3×3×3×3×3×3     the base is 3 and the power is 7

33 × 34= 37

b. 22 ×22×32

=2×2×2×2×3×3

the bases are two 2 and 3 . 2 is repeated 4  times and 3 repeated 2 times   =24×32

22 ×22×32=24×32

Example 2                

Simplify

Solution 

Write the expanded form of the following then simplify

Example 3

Using the first and second laws of indices, simplify the following and compare answers to solution 1 and solution 2. 

a. 33×34                                                     b.22×22×32

c.27 /23

Solution                           

 

 

 

 

 

 

 

 

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