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What is a Power? Topic 2.1 A POWER is an expression in the form an, where a is the BASE and n is the EXPONENT. The BASE is the number (or variable) that is multiplied by itself The EXPONENT tells you how many time you will multiply the base Examples Base = 7 Exponent = 3 Power = 73 Repeated Multiplication = 7 x 7 x 7 Examples Base = 9 Exponent = 5 Power = 95 Repeated Multiplication = 9 x 9 x 9 x 9 x 9 Examples Base = y Exponent = 4 Power = y4 Repeated Multiplication = y x y x y x y Examples Base = -3 Exponent = 4 Power = (-3)4 Repeated Mult = (-3) x (-3) x (-3) x (-3) A power with a integer base and an exponent of 2 is a SQUARE NUMBER 5cm 5x5= 52 =25 5cm 25 is a square number Example: To find the area of a square, we use s2. A power with a integer base and an exponent of 3 is a CUBE NUMBER 5cm 5cm 5cm 5x5x5= 53 =125 125 is a cube number Example: To find the volume of a cube, we use s3. Some Definitions Standard Form Simply just written as a number. No exponents! Repeated Multiplication Writing out a power as a multiplication statement. Examples Write as a POWER. a) b) 3x3x3x3x3x3x3 = 37 7 = 71 Write as a repeated multiplication and in standard form. a) b) 29 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 512 114 = 11 x 11 x 11 x 11 = 14641 Solving powers with a NEGATIVE BASE We solve it the same way. We must be careful to INCLUDE the negative sign. EX: (-3)3 = (-3) x (-3) x (-3) = -27 Is my answer positive or negative? If you have an EVEN number of negative signs your answer is POSITIVE example: (-)(-) = + (-)(-)(-)(-) = + (-9) x (-9) = 81 (-2) x (-2) x (-2) x (-2) = 16 If you have an ODD number of negative signs your answer is NEGATIVE example: (-)(+) = (-9) x (9) = -81 (-)(-)(-) = (-2) x (-2) x (-2) = -8 Examples: **Brackets are VERY Important 1) Identify the base of each power, then evaluate. a) (-3)4 base: -3 = (-3)(-3)(-3)(-3) = 81 (even # of negatives) (4) *the exponent applies to the negative sign Examples: **Brackets are VERY Important b) -34 base: 3 = (-1) (3x3x3x3) = -81 (odd # of negatives) (1) *the exponent does NOT apply to the negative sign *the negative sign in front is like multiplying by -1 (after exponent is solved – order of operations) Examples: **Brackets are VERY Important c) – (-3)4 base: -3 = (-1) (-3)(-3)(-3)(-3) = -81 (odd # of negatives) (5) *the exponent applies to the negative sign in the bracket but not the one in front of it Ways to write multiplications Use the multiplication sign (x) 7 x 7 x 7 = 343 Brackets (7)(7)(7) = 343 Variables ab = a x b = (a)(b) Making your life simpler!!! ** On your calculator use the ^ symbol to solve a power 7^3 = 343 Assignment Page 55-57 #4ac, 5ac, 7, 8, 9, 10, 13, 14acegik, 17abcd, 18a, 21a