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The Quotient Rules. x a. x a. x a. 1. =. x a – b. if a > b. 1. x a. x b. x b. 2. =. if b > a. 3. =. x 0. = 1. x b – a. The Quotient Rules. x a. =. x a – b. if a > b. 1. x b. 5. Divide. 10 13. a. 10 7. 10 13 – 7. 10 6.

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x b

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  1. The Quotient Rules xa xa xa 1 = xa –b if a > b 1. xa xb xb 2. = if b > a 3. = x0 = 1 xb –a

  2. The Quotient Rules xa = xa –b if a > b 1. xb

  3. 5. Divide. 1013 a. 107 1013 – 7 106 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 10 • 10 • 10 • 10 • 10 • 10 • 10 Count how many are crossed out. Just subtract the exponents.

  4. 5. Divide. b. x11 x x11 – 1 x10 Higher exponent in numerator. Subtract the exponents.

  5. 5. Divide. c. y18 y8 y18 – 8 y10 Higher exponent in numerator. Subtract the exponents.

  6. The Quotient Rules xa xa 1 = xa –b if a > b 1. xb xb 2. = if b > a xb –a

  7. 6. Divide. c3 a. 1 1 c4 c c4 – 3 c• c• c c• c• c• c The higher exponent is in the denominator.

  8. 6. Divide. b. 1 1031 1 1056 – 31 1056 1025 The higher exponent is in the denominator.

  9. 6. Divide. c. 1 1 z15 z6 z21 – 15 z21 The higher exponent is in the denominator.

  10. 7. Divide. x7 -7 a. 1 -21 x9 3x2 1 3 x9 – 7 Simplify. The higher exponent is in the denominator.

  11. 7. Divide. x11 15 b. -3 x4 -5 x11 – 4 1 -5x7 Simplify. The higher exponent is in the numerator.

  12. 7. Divide. x8 23 c. 1 46 x9 2x 1 2 x9 – 8 Simplify. The higher exponent is in the denominator.

  13. 8. Divide. x7 y9 a. y10 x7 y10 – 9 x7 y Can’t simplify. The higher exponent is in the denominator.

  14. 8. Divide. y6 12 x5 b. -24 x3 y8 x5 – 3 -1 2 y8 – 6 -x2 2y2 Simplify. The higher exponent is in the numerator. The higher exponent is in the denominator.

  15. The Quotient Rules xa xa xa 1 = xa –b if a > b 1. xa xb xb 2. = if b > a 3. = x0 = 1 xb –a

  16. 9. Divide. a. = 107– 7 = 100 107 107 1 Same exponent.

  17. 9. Divide. 12 a4 b. 15 a4 4 5 Simplify. Same exponent.

  18. 10. Divide. -20 a3 b8 c4 a. -5b a3 b7 c5 28 7c b8 – 7 -5 7 c5 – 4 Simplify. Same exponent. The higher exponent is in the numerator. The higher exponent is in the denominator.

  19. 10. Divide. 5 x0 y6 b. 1 x4 y8 10 2x4y2 1 2 y8– 6 x4 Simplify. 0 exponent. The higher exponent is in the denominator.

  20. 11. Simplify. ( 3 )( ) a2 b4 -6 a b5 16a5b7 a3 -18 b9 16 a5 b7 b2 -9 Multiply. 8 a2 Add the exponents in the numerator. Simplify. Subtract the exponents.

  21. The Quotient Rules xa xa xa 1 = xa –b if a > b 1. xa xb xb 2. = if b > a 3. = x0 = 1 xb –a

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