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Warm up

Warm up. Simplify the following. Warm Up. A. If two classes of 36 students each took a test with 23 questions, how many questions would Mrs. King have to grade? B. When will she have them graded?. 1656. Not today, or tomorrow…..but when she tells you they are graded.

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Warm up

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  1. Warm up • Simplify the following

  2. Warm Up • A. If two classes of 36 students each took a test with 23 questions, how many questions would Mrs. King have to grade? • B. When will she have them graded? 1656 Not today, or tomorrow…..but when she tells you they are graded

  3. Properties of Exponents Simplifying Properties of Exponents

  4. Property of Exponents Recall A is called the _____________ x is called the _____________

  5. Find the product. Write your answer as a single power. = 76 = 25 = x7 What can you conclude? When you are multiplying same bases, add the exponents.

  6. To find the power of a power… Investigation Write as a product of factors Count all factors

  7. Investigation To find the power of a power… Then write as a product of factors Count all factors What can you conclude? When you have one base, parenthesis, and two exponents, multiply the exponents.

  8. To find the power of the product… Investigation Distribute the exponent to each factor Evaluate

  9. To find the power of the product… Investigation Distribute the exponent to each factor Evaluate

  10. Zero & Negative Exponents

  11. Use your calculator to evaluate. What can you conclude? A nonzero number to the zero power equals one. • 50 • (-2)0 • (.45)0 • (1/7)0 • (1239)0 • 00

  12. PROPERTIES OF EXONENTS Zero and Negative Exponents Multiplication Properties Any nonzero number raised to the “0” power is equal to __________ Ex: (2x)0 = ______ 1 1

  13. PROPERTIES OF EXONENTS Multiplication Properties Zero and Negative Exponents How do negative exponents become positive? Negative exponents move terms to the other part of the fraction. (reciprocal)

  14. Negative exponents move terms to the other part of the fraction. (reciprocal) Example 1: Rewrite as an expression with positive exponents. x has a negative exponent. We will move the term to the other part of the fraction.

  15. x has a negative exponent. We will move the term… Example 2

  16. x as a negative exponent. We will move the term… 2 - 2 x Example 3

  17. x is downstairs. We will move it… Example 2

  18. What do we know that we can do with these exponents? What do we know that we can do with these exponents? Now let’s include what we learned from before.

  19. Evaluate the expression without using a calculator.

  20. Division Properties of Exponents

  21. Quotient of Powers Property To divide powers that have the same base, you subtract the exponents.

  22. Write out as a product of factors. Quotient of Powers Example 1: Cancel out common factors

  23. Quotient of Powers Notice what we could have done using the property. Subtract top exponent minus bottom exponent

  24. Write out as a product of factors. Quotient of Powers Example 2: Cancel out common factors

  25. Quotient of Powers Notice what we could have done using the property. Subtract top exponent minus bottom exponent Or you could say, subtract and where ever you have the larger exponent, that's where the leftovers go.

  26. Power of a Quotient Property Example 4:

  27. Example: 5

  28. Example: 6

  29. Review of Properties of Exponents • am * an = am+n • (am)n = amn • (ab)m = ambm • a-m = • = am-n • = These all work for fraction exponents as well as integer exponents.

  30. To simplify: • There are no powers of powers • There are no negative exponents • Each base appears exactly once • All fractions are in simplest form Simplifying Exponents

  31. Example 1: Simplify

  32. Example 2: Simplify

  33. Example 3: Simplify

  34. Example 4: Simplify

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