discussion about the rules of exponents in mathematics for grade 9 students

this is a full presentation for the topics exponents and the rules of it. you can use this in you daily lesson in grade 9 math students or in you classroom observation

1. UNFAMILIAR WORDS Exponent – a number that says how many times the base is to be multiplied by itself. Positive Integral Exponent – denotes a positive integer as an exponent . Negative Integral Exponent – denotes a negative integer as an exponent. Base - the number that is being multiplied by itself.

2. PARTS OF EXPONENTIAL NOTATION

3. FOR EXAMPLE Exponent form Expanded form = a•a•a•a = 2•2•2•2•2=32 = 2•2•2•3•3 = 8•9 = 72 = x•x•x•y•y•y•y  

4. Activity 1: TRANSFORM ME! Mechanics: 1. One member of the team will go to the board to answer the following expressions. They will transform it to exponent form or expanded form and simplify it as much as possible. They have 20 seconds to answer. 2. No repetition. Each member of the team should participate. 3. 1 point for every correct answer. The team with the highest point wins. In case both team have equal points. The fastest team to finish the task wins.

5. example Given answer = 3•3 2•2 = 9 • 4 = 36 a•a•a•a•b•b•b =  

6. 1. a 3 b 5 6. r•r•r•r•r•t•t•t 2. d•d•d•d•e•e•e 7. m 6 n 3 3. 2 3 8. 4•4•2•2•2 4. 3•3•3 9. z•z•z•x•x•y•y 5.2 2 5 2 10. k 4 j 5

7. ANSWERS 1. a•a•a•b•b•b•b•b 6. r 5 t 3 2. d 4 e 3 7. m•m•m•m•m•m•n•n•n 3. 8 8. 128 4. 27 9. 5 . 100 10. k•k•k•k•j•j•j•j•j ANSWERS 1. a•a•a•b•b•b•b•b 6. r 5 t 3 2. d 4 e 3 7. m•m•m•m•m•m•n•n•n 3. 8 8. 128 4. 27 5 . 100 10. k•k•k•k•j•j•j•j•j

8. Questions: 1. How is the game? 2. How did you answer every given expression? 3. What do you think is the weakness or strength of your team?

9. Remember “Every member of a team has different skills, expertise, and talent. When all the members collaborate together they are able to utilize the experience, knowledge, and skills of everyone involved to achieve the shared goal “

10. Apply the laws involving positive integral exponents to zero and negative integral exponents. 2 . Simplify exponential expressions using the laws of integral exponent.

11. Product of a Power Rule To multiply powers of the same base, keep the base and add the exponents .   Examples: Simplify each expression. 2 . 3.  

12. = =   2. = =   3. = =     SOLUTIONS

13. Power of a Power Rule To find the power of a power of a base, keep the base and multiply the exponents. EXAMPLES   = =     2. = = =       3. = = =    

14. Power of a Product Rule To find the power of a product, find the power of each factor and multiply.   EXAMPLES: = =     2. = = =       3. = = =    

15. Quotient Rule For every integer and and .   EXAMPLES: = =     2 . = =     3 . = = =    

16. Power of a Quotient Rule For every integer, and , and and .  

17. EXAMPLES =     2. = =     3. = = = =    

18. ZERO EXPONENT An expression raised to zero is equal to 1. In symbol, The expression and are called indeterminate .   =     2. = = =1     3. = =    

19. NEGATIVE INTEGRAL EXPONENT If an expression is raised to a negative exponent then it follows that; AND =   =     2. = =   3. = = 8   3 . = = = = =    

20. Activity 2: Agree or Disagree? Read each statement under the column STATEMENT then say yes master if you agree with the statement and no master if you disagree.

21. Statement Response 1. Every real number except 0 raised to zero is equal to one (1). 2. An expression with a negative exponent CANNOT be written as an expression with a positive exponent. is equal to . 6 . An expression whose base and exponent are both equal to zero is said to be indeterminate. Statement Response 1. Every real number except 0 raised to zero is equal to one (1). 2. An expression with a negative exponent CANNOT be written as an expression with a positive exponent. 6 . An expression whose base and exponent are both equal to zero is said to be indeterminate.

22. Statement Response 1. Every real number except 0 raised to zero is equal to one (1). AGREE 2. An expression with a negative exponent CANNOT be written as an expression with a positive exponent. DISAGREE is equal to . AGREE DISAGREE DISAGREE 6 . An expression whose base and exponent are both equal to zero is said to be indeterminate. AGREE Statement Response 1. Every real number except 0 raised to zero is equal to one (1). AGREE 2. An expression with a negative exponent CANNOT be written as an expression with a positive exponent. DISAGREE AGREE DISAGREE DISAGREE 6 . An expression whose base and exponent are both equal to zero is said to be indeterminate. AGREE

23. QUESTIONS: 1. What happens if the base and exponent are equal to zero? 2. What is the correct answer in number 4? 3. Why did you disagree in number 2?

24.   Activity 3 : Let’s Practice! Direction: Simplify each expression. (Notebook) 1. 2m 3 •6m 2 6. 9. (4a 2 b 3 c 4 ) 12. 3 -2 •2 -3 2. 3ab•2a 2 b 3 7. 10. 12c d 13. 3. (n 3 ) 4 8. 11. 4. ( 2x 2 y 2 z 3 ) 2 5.  

25. Answers: 1. 6. 11. 2. 7. 12. 3. 8. 13. 4. 9. 1 5. 10. 12 9. 1 10. 12

26. Activity 4 : Dig Deeper! Directions: Answer the following questions. 1. Which is the easiest part in rules of exponent? 2. What expressions can become indeterminate? 3. What do we do to the exponent when multiplying expressions? 4. How about in dividing expressions? 5. What is the effect of negative exponents? 6. How about zero exponents?

27. Importance of Exponents in real life

28. Activity 5 : TRY ME! Direction: Simplify the following.

29. ASSIGNMENT Simplify the following.  

30. REFERENCE YouTube links : https://www.youtube.com/watch?v=B1HEzNTGeZ4   https://www.youtube.com/watch?v=PApJlOrPDFg