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Chapter 4

Chapter 4. PreTest. Leave your answer in exponent form. 1. (3 6 )(3 4 ). 3 6 + 4. 3 10. Product Rule. Leave your answer in exponent form. 2 14. 2. 2 6. 2 14 – 6. 2 8. Quotient Rule. Leave your answer in exponent form. 3. (2 3 ) 5. 2 3 • 5. 2 15. Power Rules.

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Chapter 4

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  1. Chapter 4 PreTest

  2. Leave your answer in exponent form. 1.(36)(34) 36 + 4 310 Product Rule.

  3. Leave your answer in exponent form. 214 2. 26 214 – 6 28 Quotient Rule.

  4. Leave your answer in exponent form. 3.(23)5 23 • 5 215 Power Rules.

  5. Simplify. Use positive exponents. 4. ( x x3 ) 5 -2 )( y5 y3 x4 -10 y8 Multiply. Product Rule.

  6. Simplify. Use positive exponents. y4 -20 x7 5. 12 x12 y3 -5 y 3 x5 Simplify. Quotient Rules.

  7. Simplify. Use positive exponents. -3 ( ) 2 6. y5 x3 9 x6 y10 Evaluate. Power Rules.

  8. Simplify. Use positive exponents. ( )5 y2 x3 5 7. z5 3 55 x15 y10 35 z25 or x15 y10 3125 243 z25 Power Rules. Evaluate.

  9. Simplify. Use positive exponents. 15 x5 y10 8. y10 x12 10 3 2 x7 Simplify. Quotient Rules.

  10. Simplify. Use positive exponents. 9. 3-3 1 27 1 33 Negative exponents. Evaluate.

  11. Simplify. Use positive exponents. z 10. 7 x-3 y-4 z 7 x3 y4 Negative exponents.

  12. Simplify. Use positive exponents. 3 y-2 x-3 11. z-5 3 z5 x3 y2 Negative exponents.

  13. 12. Write in scientific notation. 104,000,000 104000000 . 1.04 x 108 Count the number of places to move. Positive 8 is the exponent.

  14. 13. Write in decimal notation. 1.9 x 10-3 19 000 . 0.0019 The exponent is negative 3. Move the decimal point left 3 places.

  15. 14. Multiply and write in scientific notation: ) ) ( 6.4 ( x 3.8 x 103 106 24.32 x 109 Multiply the numbers. Use the product rule.

  16. 14. Multiply and write in scientific notation: ) ) ( 6.4 ( x 3.8 x 103 106 24.32 x 109 x 109 2.432 x 101 x 2.432 1010 Write in scientific notation. Use the product rule.

  17. 15. Add. (4x2 – 5x + 2) + (6x2– 7x – 5) – 7x + 2 – 5 4x2 + 6x2 – 5x – 3 10x2 – 12x Remove both parentheses. Distribute + 1 to each term in the second parentheses. Combine like terms.

  18. 16. Subtract. – 3 ( 4x2 – + 5x ) (2x2– x + 3) – x + 3 – 4x2 + 3 – 5x 2x2 -2x2 – 6x + 6 Remove both parentheses. Distribute –1 to each term in the second parentheses. Combine like terms.

  19. 17. Multiply. ( -3 x3 x3 + 2 x2 ) – 5 3 x6 – 6 x5 -9 + 15 x3 Distribute.

  20. 18. Multiply. ( y4 x2 y2 ) -3 + 5 x2 – 6 x y3 5 + 18 x4 x3 -15 y5 y6 – 15 x2 y2 Distribute.

  21. 19. Multiply. Outer First 4x )( + 2y Last Inner ( – y 6x ) – 2y2 – 6xy 24x2 + 8xy 24x2 + 2xy – 2y2 Use FOIL to multiply. Combine like terms.

  22. 20. Multiply. 4x + 5 ( ) 4x – 5 )( (5)2 – (4x)2 16x2– 25 Special Case (a + b)(a – b) = a2 – b2 Square the first term. Subtract the square of the second term.

  23. 21. Multiply. ( 2x – 3y )2 – (2x)2 + (-3y)2 2(2x)(3y) + 9y2 4x2 – 12xy Special Case (a – b)2 = a2 – 2ab + b2 Square the first term. Subtract 2 times the first and second terms. Add the square of the second term.

  24. 22. Multiply. 2x )( – 4y3 Last Inner ( +5y2 2x4 ) Outer First – 20y5 + 10x4y2 4x5 – 8xy3 Use FOIL to multiply. No like terms.

  25. 23. Multiply. 3x – 4 ( )( ) x2 – 2x +5 – 20 + 15x – 4x2 + 8x 3x3 – 6x2 + 23x 3x3 – 20 – 10x2 Multiply each term. Combine.

  26. 24. Divide. (16x4 – 24x3 – 4x2) ÷ 4x2 x3 x2 16 24 4 x4 – – 4 4 4 x2 x2 x2 x2 – 6 x 4 – 1 Write as separate fractions. Simplify each.

  27. 25. Divide. (3x3 – 13x2 + 27x – 20) ÷ (3x – 4) x2 – 3x + 5 – 13x2 + 27x – 4 3x3 3x – 20 ) – 4x2 –( ) 3x3 -9x2 15x 3x3 + 27x -9x2 3x 3x 3x + 12x –( ) -9x2 Write as long division. 15x – 20 Divide first terms. – 20 –( ) 15x Multiply. Subtract. x2 – 3x + 5 Bring down next term.

  28. Chapter 4 Pretest

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