Form 2 Unit 1 Lesson 4: – Third and Fourth Laws of Indices

Objective

At the end of the lesson, students should be able to use the third and the fourth index laws

 

When a number which is already expressed as an exponent is raised to another power the two indices are multiplied.

In general, if a is any number and m and n are positive integers, then

Third index law:

          (am)n=amn

          (am)n=amn

 

 

Example 1

Simplify (52)3

 

Solution

(52)3= 52 × 52 × 52

= (5×5) × (5×5) × (5×5)

= 5×5×5×5×5×5

= 56

Thus (52)3=52×3=56

 

Fourth index law:

Any number (except zero) raised to the power 0 is 1.

            a0 = 1 (a≠0)

If we write 24 as the products, then we can see what happens when it is divided by itself.

 

 

Example 1

Simplify the following

a.(36)4                                                            b.  (43×33)2

 

 

Solution  

a.(36)4                                                 b.  (43× 33)2

=36×4                                                   = (43)2× (33)2

=324                                                        =43×2×33×2

                                                                               =46×36

 

 

Example 2

Simplify each of the following using the fourth index law

a. (5×6)0                      b. 80                          

 

 

Solution

a.   (5×6)0                            b. 80                           c. 27 27

= 50×60                               =                            =27-7

=1×1                                                                      =20

=                                                                          =1

 

 

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