1. The Laws of Raising a Power to a Power & Negative exponents

2. Raising a Power to a Power

3. What does this expression really mean?
(53)2

4. What does this expression really mean?
(53)2
53 ∙ 53

5. What does this expression really mean?
(53)2
53 ∙ 53
5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5

6. What does this expression really mean?
(53)2
53 ∙ 53
= 56
5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5

7. What does this expression really mean?
(53)2
= 56
53 ∙ 53
= 56
5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5

8. Let’s look at another example.
(32)4

9. Let’s look at another example.
(32)4
32 ∙ 32 ∙ 32 ∙ 32

10. Let’s look at another example.
(32)4
32 ∙ 32 ∙ 32 ∙ 32
3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3

11. Let’s look at another example.
(32)4
32 ∙ 32 ∙ 32 ∙ 32
= 38
3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3

12. Let’s look at another example.
(32)4
= 38
32 ∙ 32 ∙ 32 ∙ 32
= 38
3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3

13. From these 2 examples, we can draw a conclusion.
(53)2
= 56
(32)4
= 38

14. From these 2 examples, we can draw a conclusion.
3 ∙ 2 = 6
When raising an exponential expression to a power, simply keep the base and multiply the 2 exponents.
(53)2
= 56
2 ∙ 4 = 8
(32)4
= 38

15. Law of Raising a Power to a Power
(47 )3 = 47∙3 = 421 (33)4 = 33∙4 = 312 You try it! (2111)0 = (56)4

16. Practice Time

17. Simplify each expression.
10) (43)2 = 11) (82)4 = 12) (105)3 = 13) (c3)0 = 14) (r7)3 =

18. Simplify each expression.
10) (43)2 = ) (82)4 = 12) (105)3 = 13) (c3)0 = 14) (r7)3 =

19. Simplify each expression.
10) (43)2 = ) (82)4 = ) (105)3 = 13) (c3)0 = 14) (r7)3 =

20. Simplify each expression.
10) (43)2 = ) (82)4 = ) (105)3 = ) (c3)0 = 14) (r7)3 =

21. Simplify each expression.
10) (43)2 = ) (82)4 = ) (105)3 = ) (c3)0 = c0 or 1 14) (r7)3 =

22. Simplify each expression.
10) (43)2 = ) (82)4 = ) (105)3 = ) (c3)0 = c0 or 1 14) (r7)3 = r21

23. But what happens if you add or subtract the exponents and you get a negative number ?
First of all, there is no crying in math! Second, we have a law for that too! It’s called the Negative Rule! Let me tell you all about it…

24. Negative Rule
Any non-zero number raised to a negative power equals its reciprocal raised to the opposite positive power.
WHAT!!
Click on this button to read more about it!

25. …Negative Rule
Remember that a reciprocal is the multiplicative inverse. In simple terms, flip the fraction! The reciprocal of is .
If we apply the negative rule (Any non-zero number raised to a negative power equals its reciprocal raised to the opposite positive power) then,
A non-zero
raised to a negative power =
In this example, the negative in front of the four remains. Only the negative of the exponent is effected.
The reciprocal raised to the opposite power

26. Homework
Worktext p. 109 (2-16)even