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Unit 4: Exponents, radicals, and variation

Unit 4: Exponents, radicals, and variation. Final Exam Review. Topics to cover. Exponent Rules Converting Radicals to Fractional Exponents Converting Fractional Exponents to Radicals Solving Rational Equations Direct Variation Inverse Variation. Exponent rules.

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Unit 4: Exponents, radicals, and variation

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  1. Unit 4: Exponents, radicals, and variation Final Exam Review

  2. Topics to cover • Exponent Rules • Converting Radicals to Fractional Exponents • Converting Fractional Exponents to Radicals • Solving Rational Equations • Direct Variation • Inverse Variation

  3. Exponent rules • Mathematical Expressions can be simplified used exponent rules • Here are all of the rules: • ADDING AND SUBTRACTING EXPRESSIONS • MULTIPLYING EXPRESSIONS • RAISING A POWER TO A POWER • DIVIDING EXPRESSIONS • NEGATIVE EXPONENTS • ZERO EXPONENTS

  4. ADDING AND SUBTRACTING EXPRESSIONS • When you are adding and subtracting exponents, you must: • COMBINE LIKE TERMSonly! • Make sure to DISTRIBUTEthe NEGATIVEwhen subtracting • Example: (4x2 + 9x – 6) + (7x2 – 2x – 1) = 11x2 + 7x – 7 (3x2 + 5x – 8) – (5x2 – 4x + 6) = -2x2 + 9x – 14

  5. Multiplying expressions • When you are multiplying expressions • MULTIPLYthe whole numbers • ADDthe exponents • Example: (4x3)(2x2) = 8x5 (-4x5)(3x2) = -12x7

  6. Raising a power to a power • When you are raising a power to a power: • RAISE the whole numbers to the power • MULTIPLY the exponents • Example: (5x2)4 = 625x8 (-3x6)3 = -27x18

  7. Dividing expressions • When you are dividing expressions: • DIVIDE the whole numbers • SUBTRACT the exponents • Example: = =

  8. Negative exponents • When you have a negative exponent • MOVE the negative exponent “TO THE OTHER BUNK”, meaning, move it to the other side of the FRACTION • When you move it, change the exponent to a POSITIVEbecause now it’s “HAPPY” • Example: = = =

  9. Zero exponents • When you have a zero exponent • The answer is always ONE • Example: (5x4y2)0= 1 = 1

  10. Practice all exponent rules • (5x2 – 5x + 2) + (6x2 + 2x – 10) • (3x2 + 6x – 4) – (6x2 – 2x + 9) • (6x4)(5x2) • (4x2)3 • (3x2y)0

  11. Converting a radical into a fractional exponent • Parts of a radical • When converting a radical to a fractional exponent: • The power inside the radical becomes the NUMERATOR • The number in the INDEXbecomes the DENOMINATOR • Example:

  12. Converting a radical into a fractional exponent • Now try these:

  13. Converting a fractional exponent into a radical • When converting a fractional exponent into a radical: • The numerator becomes the power INSIDEthe radical • The denominator becomes the number in the INDEX • Example:

  14. Converting a fractional exponent into a radical • Now try these:

  15. Solving rational equations • When solving rational equations with 2 terms, you must CROSS MULTIPLY • Example: 5(2x+1) = 20x 10x + 5 = 20x 5 = 10x x =

  16. Solving rational equations • You try: Example:

  17. Direct Variation • Direct Variation is a relationship between 2 variables when 1 variable INCREASESthe other variable also INCREASES. • Equation: y = kx • K = CONSTANT

  18. Direct Variation • Example: Y varies directly as X. When y = 27, x = 6. What does y equal when x = 10? Y = kx 27 = k(6)  k = 4.5 Y = 4.5(10)  y = 45

  19. Direct Variation • You try! 1. Y varies directly as X. When y = 150, x = 35. What does y equal when x = 99? 2. The amount of money that student government makes selling homecoming t-shirts varies directly as the number of students who buy them. If SGA makes $350 when 25 people buy a shirt, how much money will they make if 55 people buy a shirt?

  20. inverse Variation • Inverse Variation is a relationship between 2 variables when 1 variable INCREASESthe other variable DECREASES. • Equation: • K = CONSTANT

  21. Inverse Variation • Example: Y varies inversely as X. When y = 18, x = 2. What does y equal when x = 12?  18  k = 36  y = 3

  22. Inverse Variation • You try! 1. Y varies inversely as X. When y = 25, x = 4.5. What does x equal when y = 10? 2. The average speed that you drive varies inversely as the time it takes to travel. It takes Sally 230 minutes to drive to Disney World when she averages 60mph. How long will it take her friend Abby to travel the same distance to Disney if she averages 53mph?

  23. ALL DONE

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