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 =1 =27-7
=1×1 =20
=1 =1