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Grade 9 Math 1.1 – What is a Power? Unit 1 – Powers & Exponent Laws We use exponents to save time when writing out long numbers. For instance, compare writing 2x2x2x2x2x2x2x2x2x2x2x2 to 212 – much easier! Exponent 224 Base Power A power with an exponent of 2 is a square number. A power with an exponent of 3 is a cube number. So, for example, you would say that 42 is “four squared” and 53 is “five cubed.” Ex. #1 Write the number of unit squares in the large square as a power. a. b. Answer: It is 5 x 5 which is 52 Answer: It is 5 x 5 x 5 which is 53 Ex. #2 Draw a picture to represent each square number. a. 2 x 2 b. 32 c. 36 Note – watch for the use of brackets, especially when there are negatives involved! When an exponent is outside of a pair of brackets, the exponent is applied to everything inside the brackets. Ex. #3 Write in exponential form. a. 3 x 3 x 3 x 3 = 34 b. -2 x -2 x -2 = (-2)3 c. 7 = 71 Ex. #4 Write as a repeated multiplication and in standard form (i.e. evaluate). a. 23 = (2)(2)(2) = 8 b. 103 = (10)(10)(10) = 1000 c. -34 = -(3)(3)(3)(3) = -81 d. (-3)4 = (-3)(-3)(-3)(-3) = 81 e. –(-3)4 = - (-3)(-3)(-3)(-3) = - 81 How to Use Your Calculator: Look for the following buttons on your calculator: x2, x3, yx, and/or ^. Ex. #5 Use your calculator to solve the following. a. 352 = 1225 b. 63 = 216 c. 87 = 2,097,152 d. 45 = 1024 Ex. #6 a. 32 = (3)(3) = 9 b. –32 = -(3)(3) = -9 c. (-3)2 = (-3)(-3) = 9 3 3 8 2 2 d. 3 27 3 3 e. 23 8 3 3 f. (0.03)2 = (0.03)(0.03) = 0.0009 When applying exponents to negative bases, notice that exponents that are even will always result in a positive answer, and exponents that are odd will always result in a negative answer. Be very careful when entering negative bases in your calculator – always use parentheses or your calculator will misunderstand what you’re trying to do! Ex. #7 Solve. a. (-3)2 = 9 b. (-3)3 = -27 c. (-2)5 = -32 d. (-2)6 = 64 Assignment Do #1 – 19 p. 55 Grade 9 Math Unit 1 – Powers & Exponent Laws 1.1 – What is a Power? Student Copy We use exponents to save time when writing out long numbers. For instance, compare writing 2x2x2x2x2x2x2x2x2x2x2x2 to _____ – much easier! _________________________ ______________ 224 __________________ A power with an exponent of 2 is a ____________ number. A power with an exponent of 3 is a ____________ number. So, for example, you would say that 42 is “four ___________” and 53 is “five ___________.” Note – watch for the use of brackets, especially when there are ___________________ involved! When an exponent is outside of a pair of brackets, the exponent is applied to everything _____________ the brackets. Ex. #1 Write the number of unit squares in the large square as a power. a. b. Ex. #2 Draw a picture to represent each square number. a. 2 x 2 b. 32 c. 36 Ex. #3 Write in exponential form. a. 3 x 3 x 3 x 3 = b. -2 x -2 x -2 = c. 7 = Ex. #4 Write as a repeated multiplication and in standard form (i.e. evaluate). a. 23 = b. 103 = c. -34 = d. (-3)4 = e. –(-3)4 = How to Use Your Calculator: Look for the following buttons on your calculator: x2, x3, yx, and/or ^. Ex. #5 Use your calculator to solve the following. a. 352 = b. 63 = c. 87 = d. 45 = Ex. #6 a. 32 = b. –32 = c. (-3)2 = d. 2 3 e. 23 3 3 f. (0.03)2 = When applying exponents to ________________ bases, notice that exponents that are ____________ will always result in a _________________ answer, and exponents that are __________ will always result in a _____________________ answer. Be very careful when entering negative bases in your calculator – always use ________________ or your calculator will misunderstand what you’re trying to do! Ex. #7 Solve. a. (-3)2 = b. (-3)3 = c. (-2)5 = d. (-2)6 = Assignment Do #1 – 19 p. 55