The document is a lesson plan on exponents and radicals that includes: 1. An agenda covering questions from homework, an upcoming quiz, and lessons on exponents and radicals. 2. Sections on properties of integer exponents, simplifying expressions with exponents, negative exponents, and challenges involving exponents. 3. Discussions of rational exponents and how they relate to radicals, properties of radicals, and examples rewriting expressions using exponents and radicals. 4. Classwork assignments for students to complete.

1. Today’s Agenda
• Attendance / Announcements
• Questions from HW?
• Quiz Tomorrow (1.3 – 1.5)
• Section 1.5 Exponents and Radicals

2. Exponents…continued
More Properties of Integer
Exponents

3. Exponents…continued
More Properties of Integer
Exponents

4. Simplify…

5. Simplify…(a lil‟ trick.)
5
2
2
16
3
3
9
27

6. Exponents…continued
More Properties of Integer
Exponents

7. Simplify…

8. Exponents…continued
Negative Exponents
We usually want our answers to be
written only in Positive
Exponents…So we need to rewrite.

9. Simplify…

10. Exponents…continued
Negative Exponents

11. Simplify…
2
2
y
x
2
3
4
3
z
yx

12. ¡CHALLENGE !
43231
34 xx

13. ¡CHALLENGE !
3
24
23
5
y
x
x
x

14. Properties of Exponents
• You‟ll need to know the entire
list on page 41.

15. Classwork…Part I
• Page 46
1 – 21 every other odd
43 – 49 odd
...Ask questions if you have
„em!

16. Rational Exponents  Radicals
You can think of fraction exponents
as radicals…and vice versa

17. Rational Exponents (p. 44)
So, if n is an even integer and a ≥ 0;
or if n is odd, then
n
aan
1
When dealing with radicals/roots, we
always need to think about…

18. Rational Exponents  Radicals
And if the root exists…
n
m
aan m
An example of when the root doesn’t
exist…

19. Rewrite in radical notation
3
2
x 4
3
)3( y

20. Rewrite in exponent notation
5
x 3
7 3
3 x

21. Rational Exponents  Radicals
Another Way to simplify
5
2
32

22. Properties of Radicals (p. 44)
Radicals can be separated across
multiplication and division.

23. Properties of Radicals
We use these properties when we
simplify roots.
72

24. Properties of Radicals
80245205
Remember, we can only add “like”
terms

25. Properties of Radicals
2353

26. Classwork / Homework
•Page 34
1 – 87 every other odd
...Ask questions if you have
„em!