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PRETEST

PRETEST. Unit 3 Exponents and Logarithms. Warm up. Simplify the following. Properties of Exponents. Simplifying Properties of Exponents. Property of Exponents. Recall . A is called the _____________. x is called the _____________.

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PRETEST

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  1. PRETEST

  2. Unit 3 Exponents and Logarithms

  3. Warm up • Simplify the following

  4. Properties of Exponents Simplifying Properties of Exponents

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

  6. 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.

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

  8. 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.

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

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

  11. Zero & Negative Exponents

  12. 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

  13. Negative EXPONENTS Negative exponents move terms to the other part of the fraction (Change location and become positive)

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

  23. 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.

  24. Power of a Quotient Property Example 4:

  25. Example: 5

  26. Example: 6

  27. 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.

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

  29. Example 1: Simplify

  30. Example 2: Simplify

  31. Example 3: Simplify

  32. Example 4: Simplify

  33. Homework

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