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Notes: Exponents and Square Roots Name___________KEY_______________Per___Date __________ Exponents Fill in the blanks with the names. Use your past notes to help you. 43 Exponent – tells how many times the ____________________ is used as a factor (multiplied.) Power – a number that can be expressed using an __________________________. Write using exponents: 1) 8 . 8 . 8 . 8 . 8 .= 2) 10 . 10 . 10 . 10 . 10 . 10 . 10 . 10 = Write as a product of repeated factors. Then simplify. 34 = 3 . 3 . 3 . 3 = _____ 104 = 10 . 10 . 10 . 10 = _____ 33 = _________ = _____ 103 = ____________ = _____ 32 = _________ = _____ 102 = ____________ = _____ 31 = _________ = _____ 101 = ____________ = _____ 30 = _____ 100 = _____ Look at the patter to find the zero powers!!! I. Square Roots and Irrational Numbers Vocabulary: Perfect Square – a number that is the second power (square) of an integer. Examples: 32= 9 so 9 is a perfect square. Square Root – a number that when multiplied by itself (when it is squared) forms a product that is a perfect square. The symbol (a radical) means: “what number times itself (squared) gives you the number under the radical symbol?” 1. Calculate the following: 25 = 9 = 16 = 12 12 is called an irrational number. Irrational number - a decimal number that neither terminates, nor repeats. Rational number – can be written as a ratio (fraction) and as a decimal it terminates or repeats. Tell if these numbers are rational or irrational and why. 14 100 -0.98 0.323223222322223…… 0.232323232323…. π Why is any Number to the Zero Power Equal to 1? Fill in the table. 2 0= 1 2 1= 2 2= 2 3= 2 4= 2 5= 2 6= 2 7= 2 8= 2 0= 2 4= 2 3= 2 2= 2 1= 2 0= What is an easy way to find the next factor? Now fill in the table using the information above. 2 9= 2 8= 2 7= 2 6= 2 5= As you move to the right in the table what is the pattern?_____________________________________ When you get to 21 what will you do to that product to move to 20?___________________________ What about the pattern for : 34 = , 33 = , 32 = , 31 = , 30 = 44 = , 43 = , 42 = , 41 = , 40 = 54 = , 53 = , 52 = , 51 = , 50 = 104 = , 103 = , 102 = , 101 = , 100 = Should this pattern work for any number to the zero power?__________________________________ Notes: Exponents and Square Roots Name_______________________________Per___Date __________ Exponents Fill in the blanks with the names. Use your past notes to help you. 43 Exponent – tells how many times the ____________________ is used as a factor (multiplied.) Power – a number that can be expressed using an __________________________. Write using exponents: 2) 8 . 8 . 8 . 8 . 8 .= 2) 10 . 10 . 10 . 10 . 10 . 10 . 10 . 10 = Write as a product of repeated factors. Then simplify. 34 = 3 . 3 . 3 . 3 = _____ 104 = 10 . 10 . 10 . 10 = _____ 33 = _________ = _____ 103 = ____________ = _____ 32 = _________ = _____ 102 = ____________ = _____ 31 = _________ = _____ 101 = ____________ = _____ 30 = _____ 100 = _____ Look at the patter to find the zero powers!!! II. Square Roots and Irrational Numbers Vocabulary: Perfect Square – a number that is the _____________________ power (square) of an integer. Examples: 32= 9 so 9 is a ________________________ square. Square Root – a number that when multiplied by itself (when it is ________________________) forms a product that is a perfect square. The symbol (a ____________________) means: “what number times itself (squared) gives you the number under the radical symbol?” 2. Calculate the following: 25 = 9 = 16 = 12 12 is called an irrational number. Irrational number - a decimal number that neither ______________________, nor repeats. Rational number – can be written as a __________________ (fraction) and as a decimal it terminates or repeats. Tell if these numbers are rational or irrational and why. 14 100 -0.98 0.323223222322223…… 0.232323232323…. π Why is any Number to the Zero Power Equal to 1? Fill in the table. 2 0= 1 2 1= 2 2= 2 3= 2 4= 2 5= 2 6= 2 7= 2 8= 2 0= 2 4= 2 3= 2 2= 2 1= 2 0= What is an easy way to find the next factor? Now fill in the table using the information above. 2 9= 2 8= 2 7= 2 6= 2 5= As you move to the right in the table what is the pattern?_____________________________________ When you get to 21 what will you do to that product to move to 20?___________________________ What about the pattern for : 34 = , 33 = , 32 = , 31 = , 30 = 44 = , 43 = , 42 = , 41 = , 40 = 54 = , 53 = , 52 = , 51 = , 50 = 104 = , 103 = , 102 = , 101 = , 100 = Should this pattern work for any number to the zero power?__________________________________ Practice using EXPONENTS Name_______________________________ Period________ Date __________________ Write using exponents. 1. 3 . 3 . 3 . 3. 3 = _____ 2. 2.7 . 2.7 . 2.7 = _____ 3. 11.6 . 11.6 . 11.6 . 11.6 = _____ 4. 2 . 2 . 2 . 2 . 2 . 2 = _____ 5. 4 . 4 . 4 . 4 . 4 . 4 . 4 . 4 = _____ Write as the product of repeated factors. Then simplify. 6. 24 = ______________________________________ = _________ 7. 53 = ______________________________________ = _________ 8. (0.5)3 = ______________________________________ = _________ 9. 105 = ______________________________________ = _________ 10. Fill in the blanks with <, >, or =. Show what each is equal to in order to verify your answer. 9 = 3 . 3 = 32 < 23 42 24 52 25 62 26 43 34 53 35 72 27 =2. 2.2=8 11. What do you notice usually happens as the exponent gets bigger and the base is smaller? __________________________________________________________________________