# Exponents Intro with Practice.ppt

math 9

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### Exponents Intro with Practice.ppt

• 2. Exponent used to show repeated multiplication of a number by itself. 3 4 Base Exponent
• 3. Definition of Exponent An exponent tells how many times a number is multiplied by itself. 3 4 Base Exponent
• 4. What an Exponent Represents  the exponent stands for the number of times the number is multiplied to itself. 3 4 = 3 x 3 x 3 x 3
• 5. How to read an Exponent This exponent is read three to the fourth power. 3 4 Base Exponent
• 6. How to read an Exponent This exponent is read three to the 2nd power or three squared. 3 2 Base Exponent
• 7. How to read an Exponent This exponent is read three to the 3rd power or three cubed. 3 3 Base Exponent
• 8. Read These Exponents 3 2 6 7 2 3 5 4
• 9. What is the Exponent? 2 x 2 x 2 = 2 3
• 10. What is the Exponent? 3 x 3 = 3 2
• 11. What is the Exponent? 5 x 5 x 5 x 5 = 5 4
• 12. What is the Base and the Exponent? 8 x 8 x 8 x 8 = 8 4
• 13. What is the Base and the Exponent? 7 x 7 x 7 x 7 x 7 =7 5
• 14. What is the Base and the Exponent? 9 x 9 = 9 2
• 15. How to Multiply Out an Exponent to Find the Standard Form = 3 x 3 x 3 x 3 3 9 27 81 4
• 16. What is the Base and Exponent in Standard Form? 4 2 = 16
• 17. What is the Base and Exponent in Standard Form? 2 3 = 8
• 18. What is the Base and Exponent in Standard Form? 3 2 = 9
• 19. What is the Base and Exponent in Standard Form? 5 3 = 125
• 20. Common Mistake 25 ≠(does not equal) 2 x 5 25 ≠(does not equal)10 25 =2 x 2 x 2 x 2 x
• 21. Common Mistake -24 ≠(does not equal)(-2)4 Without the parenthesis, positive 2 is multiplied by itself 4 times; then the answer is negative. With the parenthesis, negative 2 is multiplied by itself 4 times; then the answer becomes positive.
• 22. Common mistake -24 = (-1)x(x means times) +24 = Why? The 1 and the positive sign are invisible. Anything x 1=anything, so 1 x 2 x 2 x 2 x 2 = 16; and negative x positive = negative
• 23. Common Mistake (-2)4=- 2 x -2 x -2 x -2 = +16 Why? Multiply the numbers: 2 x 2 x 2 x 2 = 16 and then multiply the signs: 1st negative x 2nd negative = positive; that positive x 3rd negative = negative; that negative x 4th negative = positive; so answer = positive 16
• 25. The Laws of Exponents: #1: Exponential form: The exponent of a power indicates how many times the base multiplies itself. n n times x x x x x x x x         3 Example: 5 5 5 5    n factors of x
• 26. #2: Multiplying Powers: If you are multiplying Powers with the same base, KEEP the BASE & ADD the EXPONENTS! m n m n x x x    512 2 2 2 2 9 3 6 3 6      So, I get it! When you multiply Powers, you add the exponents!
• 27. #3: Dividing Powers: When dividing Powers with the same base, KEEP the BASE & SUBTRACT the EXPONENTS! m m n m n n x x x x x     So, I get it! When you divide Powers, you subtract the exponents! 16 2 2 2 2 4 2 6 2 6    
• 28. Try these:   2 2 3 3 . 1   4 2 5 5 . 2   2 5 . 3 a a   7 2 4 2 . 4 s s     3 2 ) 3 ( ) 3 ( . 5   3 7 4 2 . 6 t s t s  4 12 . 7 s s  5 9 3 3 . 8  4 4 8 12 . 9 t s t s  5 4 8 5 4 36 . 10 b a b a
• 29.   2 2 3 3 . 1   4 2 5 5 . 2   2 5 . 3 a a   7 2 4 2 . 4 s s     3 2 ) 3 ( ) 3 ( . 5   3 7 4 2 . 6 t s t s 81 3 3 4 2 2    7 2 5 a a   9 7 2 8 4 2 s s     SOLUTIONS 6 4 2 5 5   243 ) 3 ( ) 3 ( 5 3 2       7 9 3 4 7 2 t s t s   
• 31. #4: Power of a Power: If you are raising a Power to an exponent, you multiply the exponents!   n m mn x x  So, when I take a Power to a power, I multiply the exponents 5 2 3 2 3 5 5 ) 5 (   
• 32. #5: Product Law of Exponents: If the product of the bases is powered by the same exponent, then the result is a multiplication of individual factors of the product, each powered by the given exponent.   n n n xy x y   So, when I take a Power of a Product, I apply the exponent to all factors of the product. 2 2 2 ) ( b a ab 
• 33. #6: Quotient Law of Exponents: If the quotient of the bases is powered by the same exponent, then the result is both numerator and denominator , each powered by the given exponent. n n n x x y y        So, when I take a Power of a Quotient, I apply the exponent to all parts of the quotient. 81 16 3 2 3 2 4 4 4        
• 34. Try these:    5 2 3 . 1    4 3 . 2 a    3 2 2 . 3 a    2 3 5 2 2 . 4 b a   2 2 ) 3 ( . 5 a    3 4 2 . 6 t s        5 . 7 t s          2 5 9 3 3 . 8          2 4 8 . 9 rt st          2 5 4 8 5 4 36 . 10 b a b a
• 35.    5 2 3 . 1    4 3 . 2 a    3 2 2 . 3 a    2 3 5 2 2 . 4 b a   2 2 ) 3 ( . 5 a    3 4 2 . 6 t s SOLUTIONS 10 3 12 a 6 3 2 3 8 2 a a   6 10 6 10 4 2 3 2 5 2 2 16 2 2 b a b a b a        4 2 2 2 9 3 a a     12 6 3 4 3 2 t s t s   
• 37. #7: Negative Law of Exponents: If the base is powered by the negative exponent, then the base becomes reciprocal with the positive exponent. 1 m m x x   So, when I have a Negative Exponent, I switch the base to its reciprocal with a Positive Exponent. Ha Ha! If the base with the negative exponent is in the denominator, it moves to the numerator to lose its negative sign! 9 3 3 1 125 1 5 1 5 2 2 3 3       and
• 38. #8: Zero Law of Exponents: Any base powered by zero exponent equals one. 0 1 x  1 ) 5 ( 1 1 5 0 0 0    a and a and So zero factors of a base equals 1. That makes sense! Every power has a coefficient of 1.
• 39. Try these:    0 2 2 . 1 b a   4 2 . 2 y y    1 5 . 3 a    7 2 4 . 4 s s      4 3 2 3 . 5 y x    0 4 2 . 6 t s          1 2 2 . 7 x          2 5 9 3 3 . 8          2 4 4 2 2 . 9 t s t s          2 5 4 5 4 36 . 10 b a a
• 40. SOLUTIONS    0 2 2 . 1 b a    1 5 . 3 a    7 2 4 . 4 s s      4 3 2 3 . 5 y x    0 4 2 . 6 t s 1 5 1 a 5 4s   12 8 12 8 4 81 3 y x y x    1
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