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Simplifying Exponents

Simplifying Exponents. Algebra I. Contents. Multiplication Properties of Exponents ……….1 – 13 Zero Exponent and Negative Exponents……14 – 24 Division Properties of Exponents ……………….15 – 32 Simplifying Expressions using Multiplication and Division Properties of Exponents…………………33 – 51

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Simplifying Exponents

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  1. Simplifying Exponents Algebra I

  2. Contents • Multiplication Properties of Exponents ……….1 – 13 • Zero Exponent and Negative Exponents……14 – 24 • Division Properties of Exponents ……………….15 – 32 • Simplifying Expressions using Multiplication and Division Properties of Exponents…………………33 – 51 • Scientific Notation ………………………………………..52 - 61

  3. Multiplication Properties of Exponents • Product of Powers Property • Power of a Power Property • Power of a Product Property

  4. Product of Powers Property • To multiply powers that have the same base, you add the exponents. • Example:

  5. Practice Product of Powers Property: • Try: • Try:

  6. Answers To Practice Problems • Answer: • Answer:

  7. Power of a Power Property • To find a power of a power, you multiply the exponents. • Example: • Therefore,

  8. Practice Using the Power of a Power Property • Try: • Try:

  9. Answers to Practice Problems • Answer: • Answer:

  10. Power of a Product Property • To find a power of a product, find the power of EACH factor and multiply. • Example:

  11. Practice Power of a Product Property • Try: • Try:

  12. Answers to Practice Problems • Answer: • Answer:

  13. Review Multiplication Properties of Exponents • Product of Powers Property—To multiply powers that have the same base, ADD the exponents. • Power of a Power Property—To find a power of a power, multiply the exponents. • Power of a Product Property—To find a power of a product, find the power of each factor and multiply.

  14. Zero Exponents • Any number, besides zero, to the zero power is 1. • Example: • Example:

  15. Negative Exponents • To make a negative exponent a positive exponent, write it as its reciprocal. • In other words, when faced with a negative exponent—make it happy by “flipping” it.

  16. Negative Exponent Examples • Example of Negative Exponent in the Numerator: • The negative exponent is in the numerator—to make it positive, I “flipped” it to the denominator.

  17. Negative Exponents Example • Negative Exponent in the Denominator: • The negative exponent is in the denominator, so I “flipped” it to the numerator to make the exponent positive.

  18. Practice Making Negative Exponents Positive • Try: • Try:

  19. Answers to Negative Exponents Practice • Answer: • Answer:

  20. Rewrite the Expression with Positive Exponents • Example: • Look at EACH factor and decide if the factor belongs in the numerator or denominator. • All three factors are in the numerator. The 2 has a positive exponent, so it remains in the numerator, the x has a negative exponent, so we “flip” it to the denominator. The y has a negative exponent, so we “flip” it to the denominator.

  21. Rewrite the Expression with Positive Exponents • Example: • All the factors are in the numerator. Now look at each factor and decide if the exponent is positive or negative. If the exponent is negative, we will flip the factor to make the exponent positive.

  22. Rewriting the Expression with Positive Exponents • Example: • The 4 has a negative exponent so to make the exponent positive—flip it to the denominator. • The exponent of a is 1, and the exponent of b is 3—both positive exponents, so they will remain in the numerator. • The exponent of c is negative so we will flip c from the numerator to the denominator to make the exponent positive.

  23. Practice Rewriting the Expressions with Positive Exponents: • Try: • Try:

  24. Answers • Answer • Answer

  25. Division Properties of Exponents • Quotient of Powers Property • Power of a Quotient Property

  26. Quotient of Powers Property • To divide powers that have the same base, subtract the exponents. • Example:

  27. Practice Quotient of Powers Property • Try: • Try:

  28. Answers • Answer: • Answer:

  29. Power of a Quotient Property • To find a power of a quotient, find the power of the numerator and the power of the denominator and divide. • Example:

  30. Simplifying Expressions • Simplify

  31. Simplifying Expressions • First use the Power of a Quotient Property along with the Power of a Power Property

  32. Simplify Expressions • Now use the Quotient of Power Property

  33. Simplify Expressions • Simplify

  34. Steps to Simplifying Expressions • Power of a Quotient Property along with Power of a Power Property to remove parenthesis • “Flip” negative exponents to make them positive exponents • Use Product of Powers Property • Use the Quotient of Powers Property

  35. Power of a Quotient Property and Power of a Power Property • Use the power of a quotient property to remove parenthesis and since the expression has a power to a power, use the power of a power property.

  36. Continued • Simplify powers

  37. “Flip” Negative Exponents to make Positive Exponents • Now make all of the exponents positive by looking at each factor and deciding if they belong in the numerator or denominator.

  38. Product of Powers Property • Now use the product of powers property to simplify the variables.

  39. Quotient of Powers Property • Now use the Quotient of Powers Property to simplify.

  40. Simplify the Expression • Simplify:

  41. Step 1: Power of a Quotient Property and Power of a Power Property

  42. Step 2: “Flip” Negative Exponents

  43. Step 3: Product of Powers Property

  44. Step 4: Quotient of Powers Property

  45. Simplifying Expressions • Given • Step 1: Power of a Quotient Property

  46. Power of Quotient Property • Result after Step 1: • Step 2: Flip Negative Exponents

  47. Step 3: Make one large Fraction by using the product of Powers Property “Flip” Negative Exponents

  48. Make one Fraction by Using Product of Powers Property

  49. Use Quotient of Powers Property

  50. Simplify the Expressions • Try: • Try:

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