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B11 Exponents and Scientific Notation

B11 Exponents and Scientific Notation. Multiplying Powers with Like Bases. For any rational number a, and for all whole numbers m and n,. Example 1. Simplify. Express using exponents. a). b). c). d). Practice. Simplify. Express using exponents. a). b). c). d).

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B11 Exponents and Scientific Notation

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  1. B11Exponents and Scientific Notation

  2. Multiplying Powers with Like Bases For any rational number a, and for all whole numbers m and n,

  3. Example 1 Simplify. Express using exponents. a) b) c) d)

  4. Practice Simplify. Express using exponents. a) b) c) d)

  5. Dividing Powers with Like Bases For any rational number a except 0, and for all whole numbers m and n,

  6. Example 2 Simplify. Express using exponents. a) b) c)

  7. Practice Simplify. Express using exponents. a) b) c)

  8. Negative Exponents For any rational number a except 0, and for all whole numbers m and n,

  9. Example 3 Express using positive exponents. a) b) c) d)

  10. Practice Express using exponents. 1) 2) 3)

  11. The Exponent Zero a0 = 1 for any rational number a except 0.

  12. Example 4 Simplify. a) b) c) d)

  13. Practice Simplify. 1) 2) 3)

  14. Practice Write without exponents. 1) 2) 3) Simplify. Express using exponents. 4) 5)

  15. Raising a Power to a Power For any rational number a, and any whole numbers m and n,

  16. Example 1 Simplify. Express using exponents. (52)3 = 56 (45)6 = 430 (x4)7 = x28

  17. Practice Simplify. Express using exponents. 1) (54)3 2) (22)5 3) (a6)3 4) (n4)4

  18. Example 2 Simplify. (5x)3 = (5x)(5x)(5x) = 125x3 (3z)2 = (3z)(3z) = 9z2 (2y2)4 = (2y2)(2y2)(2y2)(2y2) = 16y8

  19. Practice Simplify. 1) (3y)2 2) (6m)4 3) (2a3)3 4) (4x3)2

  20. Example 3 Simplify. (4x5y2)3 = 43x15y6 = 64x15y6 (-2x5y2)7 = -27x35y14 = -128x35y14 (2y2)4 = (2y2)(2y2)(2y2)(2y2) = 16y8

  21. Practice Simplify. 1) (4y3)4 2) (3x4y7z6)5 3) (-7x9y6)2

  22. Example 4 Simplify.

  23. Practice Simplify 3) (3x5)4 1) (34)3 2) (6x)3 5) 4) (-3m4n2)2

  24. Multiplying and Dividing Monomials

  25. Example 1 Multiply. (7y)(2y) = (7)(2)(y)(y) = 14y2 (5a3)(3a2) = (5)(3)(a3)(a2) = 15a5 (-3x3)(4xy5) = (-3)(4)(x3)(x)(y5) = -12x4y5

  26. Practice Multiply. 1) (3x)(-5) 2) (-m)(m) 3) (-x)2x3 4) (3p5q2)(4p2q3)

  27. Practice Multiply. 5) (4x5y5)(-2x6y4) 6) (-7y4)(-y)(2y3) 7) (7a5)(3a3)(-a5) 8) (9b2)(2b5)(-3b7)

  28. Example 2 Divide. 3 a 5 = 4 3 b 2 = a 2

  29. Practice Divide. 1) 2) 3) 4)

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