# 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

Lesson Content
error: Content is protected !!