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What is a Power?

What is a Power?. Topic 2.1. A POWER is an expression in the form a n , 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. 7 3. Examples. Base = 7

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What is a Power?

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  1. What is a Power? Topic 2.1

  2. A POWER is an expression in the form an, where a is the BASE and n is the EXPONENT. • The BASEis the number (or variable) that is multiplied by itself • The EXPONENT tells you how many time you will multiply the base

  3. 73 Examples • Base = 7 • Exponent = 3 • Power = 73 • Repeated Multiplication = 7 x 7 x 7

  4. 95 Examples • Base = 9 • Exponent = 5 • Power = 95 • Repeated Multiplication = 9 x 9 x 9 x 9 x 9

  5. y4 Examples • Base = y • Exponent = 4 • Power = y4 • Repeated Multiplication = y x y x y x y

  6. (-3)4 Examples • Base = -3 • Exponent = 4 • Power = (-3)4 • Repeated Mult = (-3) x (-3) x (-3) x (-3)

  7. A power with a integer base and an exponent of 2 is a SQUARE NUMBER Example: To find the area of a square, we use s2. 5cm 5x5= 52 =25 25 is a square number 5cm

  8. A power with a integer base and an exponent of 3 is a CUBE NUMBER 5cm Example: To find the volume of a cube, we use s3. 5x5x5= 53 =125 125 is a cube number 5cm 5cm

  9. Some Definitions • Standard Form  Simply just written as a number. No exponents! • Repeated Multiplication  Writing out a power as a multiplication statement.

  10. Examples Write as a POWER. • 3x3x3x3x3x3x3 = • 7 = Write as a repeated multiplication and in standard form. • 29 = • 114 = 37 71 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 512 11 x 11 x 11 x 11 = 14641

  11. 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

  12. 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

  13. 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

  14. 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)

  15. 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

  16. 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)

  17. Making your life simpler!!! ** On your calculator use the ^ symbol to solve a power 7^3 = 343

  18. Assignment Page 55-57 #4ac, 5ac, 7, 8, 9, 10, 13, 14acegik, 17abcd, 18a, 21a

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