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PreTest Chapter 4

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Leave your answer in exponent form. 1.(3 6 )(3 4 ) 3 6 + 4 3 10 Product Rule.

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2 14 – 6 2828 2. 2626 2 14 Leave your answer in exponent form. Quotient Rule.

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3.(2 3 ) 5 2 3 5 2 15 Leave your answer in exponent form. Power Rules.

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Simplify. Use positive exponents. 4.( - 10 -2-2 x y3y3 5 )( x3x3 y5y5 ) y 8 x 4 Multiply. Product Rule.

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5. 12 -20 3 -5y x 5 Simplify. Use positive exponents. x7x7 y4y4 x 12 y3y3 Simplify. Quotient Rules.

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6. 9 x 6 y 10 Simplify. Use positive exponents. ( - 3 x 3 y 5 2 ) Power Rules. Evaluate.

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( ) 5 7. 3 5 or 5 5 x 15 y 10 3 5 z 25 3125 x 15 y 10 243z 25 Simplify. Use positive exponents. x3x3 y2y2 z5z5 Evaluate. Power Rules.

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8. 10 15 3 2x7x7 Simplify. Use positive exponents. Quotient Rules. Simplify. x 12 x5x5 y 10

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

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10. 7 x3x3 y4y4 z Simplify. Use positive exponents. 7 x -3 y -4 z Negative exponents.

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3 x3x3 y2y2 z 5 11. z -5 3 Simplify. Use positive exponents. y -2 x -3 Negative exponents.

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12. Write in scientific notation. 104,000,000 104000000. x 10 8 1.04 Count the number of places to move. Positive 8 is the exponent.

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

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14. Multiply and write in scientific notation: ) 3.8 ( 24.32 x 10 9 ( 6.4 x 10 3 ) x 10 6 Use the product rule. Multiply the numbers.

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) 3.8 ( 24.32 x 10 9 (6.4 x 10 3 ) x 10 6 Use the product rule. Write in scientific notation. 2.432 x x 10 9 2.432 x 10 10 10 1

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

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

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17. Multiply. ( x 3 - 3 x 3 + 2x 2 ) - 9x 6 – 6x 5 – 5 + 15x 3 Distribute. 3

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18. Multiply. -3-3 - 15x 4 + 18x 3 – 15x 2 y 5 y 6 y 2 x2x2 y2y2 ( x2x2 – 6 x y4y4 )+ 5 Distribute. 5 y3y3

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

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

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

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22. Multiply. Last First ( 4x 5 + 10x 4 y 2 – 20y 5 – 8xy 3 Outer Inner Use FOIL to multiply. No like terms. 2x + 5y 2 )( 2x 4 – 4y 3 )

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23. Multiply. ( )( ) 3x 3x 3 – 20+ 15x+ 8x– 6x 2 – 4x 2 3x 3 – 4 x2x2 – 2x + 5 – 10x 2 + 23x – 20 Multiply each term. Combine.

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(16x 4 – 24x 3 – 4x 2 ) ÷ 4x 2 24. Divide. 4 – – 16 4 – 24 4 – 4 4 x 2 x6 1 x 4 x 2 x 2 x 3 x 2 x 2 Write as separate fractions. Simplify each.

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(3x 3 – 13x 2 + 27x – 20) ÷ (3x – 4) 25. Divide. –( ) 3x 3 –( ) 3x ) 3x 3 3x x 2 3x 3 -9x 2 + 27x -9x 2 3x – 3x -9x 2 15x– 20 15x 3x + 5 –( )15x x 2 – 3x + 5 – 4x 2 + 12x – 20 – 13x 2 + 27x – 20 – 4 Divide first terms. Multiply. Subtract. Bring down next term. Write as long division.

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