1. Rational Exponents, Radicals, Growth and Decay

2. The value under the radical symbol
Fractional Exponents
“Index”
“Radical Symbol”
“Radicand”
The value under the radical symbol

3. Exponent Rules

4. NEGATIVE EXPONENT RULE
Upstairs – Downstairs: A negative exponent means it’s in the wrong place.

5. PRODUCT PROPERTY FOR EXPONENTS
YOU HAVE TO HAVE THE SAME BASE TO USE
THE PRODUCT RULE

6. QUOTIENT PROPERTY FOR EXPONENTS
YOU HAVE TO HAVE THE SAME BASE TO USE
THE QUOTIENT RULE

7. POWER PROPERTY FOR EXPONENTS

8. POWER OF PRODUCT PROPERTY

9. POWER OF A QUOTIENT PROPERT

10. POWER OF QUOTIENT 2 RULE

11. RATIONAL EXPONENT RULE
Both methods are correct, but the second method requires you to break down
a much bigger number.

12. RADICAL TO EXPONENT RULE
Since square roots are the most common root we don’t write the “2”
in the radical symbol. We understand that it is there.

13. Let’s put a few ideas together
Convert the decimal to a fraction

14. Let’s Try Some
Hint: convert to a fraction rather than a decimal!

15. Exponential Growth and Decay

16. Exponential Growth and Decay

17. Link to Regents Growth and Decay Page

18. Investigation: Tournament Play
The NCAA holds an annual basketball tournament every March.
The top 64 teams in Division I are invited to play each spring.
When a team loses, it is out of the tournament.
Work with a partner close by to you and answer the following questions.

19. Investigation: Tournament Play
After round x
Number of teams in tournament (y) 64 1 2 3 4 5 6
Fill in the following chart and then graph the results on a piece of graph paper.
Then be prepared to interpret what is happening in the graph.

20. A population of 20 rabbits is released into a wildlife region
A population of 20 rabbits is released into a wildlife region. The population triples each year for 5 years.
Work with a partner close by to you and answer the following questions.

21. Investigation: Rabbit Population
After year
Number of rabbits (y) 1 2 3 4 5
Fill in the following chart and then graph the results on a piece of graph paper.
Then be prepared to interpret what is happening in the graph.