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9.1 Zero and Negative Exponents

9.1 Zero and Negative Exponents. Warm Up: Complete the tables by finding the value of each power. What happens to the value of the expression each time the exponent decreases?.

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9.1 Zero and Negative Exponents

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  1. 9.1 Zero and Negative Exponents

  2. Warm Up: Complete the tables by finding the value of each power.

  3. What happens to the value of the expression each time the exponent decreases? In table 1, each time the exponent decreases, the value of the expression is divided by 2. In table 2, the value of the expression is divided by 3. In table 3, the value of the expression is divided by 4.

  4. Predict: Continue to follow the pattern in Column 2 of each table. What will the value of 20, 30, and 40 be? Keypoint#1: For any number a, a0 = ______. 1 1 1 Based on the patterns you’ve observed above, complete the following rule: 1

  5. Predict: Continue to follow the pattern in Column 2 of each table. What will be the value of each base to the -1 power, -2 power, etc.?

  6. Compare the value of 23 to the value of 2-3. Now compare 22 and 2-2. Now compare 21 and 2-1. What do you notice? If two powers have the same base but opposite exponents (ex. 44 , 4-4) how are their values related? If two powers have the same base, but opposite exponents, then their powers are reciprocals.

  7. Based on your observation in #5, if you know that 212 = 4096, predict the value of 2-12. Based on our observation 2-12 should be the reciprocal of 212 so 2-12 = 1/4096.

  8. Based on the patterns you’ve observed above, complete the following rule: Keypoint#2: For any number a and integer n, a-n= ______.

  9. Keypoint #3: multiply • Positive exponents tell you how many times you ______________ by the base. Ex. 64 = • Negative exponents tell you how many times you ______________ by the base. Ex. 6-4 = divide

  10. Keypoint #4: • Negative exponents DO NOT create ______________ answers. • Negative exponents create ______________ answers. Ex. 8-2 = negative fractional

  11. Try These: Write each expression as a simple fraction.

  12. Simplified expressions are written with positive exponents 3 3 Does the -3 exponent apply just to the x or to the entire 4yx? Hmmm…How would I change the original if I wanted the -3 exponent to apply to the entire 4yx?

  13. Simplified expressions are written with positive exponents I know that a fraction bar means DIVIDE. -4 4 Dividing is the same as multiplying by the reciprocal. 4 4

  14. Try These: Fill in every box with the correct exponent in order to rewrite each expression so that all exponents are positive.(Four questions in your notes)

  15. Based on the examples and practice above, complete the following: Keypoint #5: If a number has a negative exponent in the numerator, it will be rewritten with a positive exponent in the _______________________. If a number has a negative exponent in the denominator, it will be rewritten with a positive exponent in the _______________________. denominator numerator

  16. Predict how the expression below will simplify with only positive exponents. .

  17. Classwork: Matching Equivalent Expressions (10 min) Work with your neighbor in 12-inch voices. Match each expression with the simplified expression. Each answer may only be used once. Talk out your thought process. Things I Should Hear: “I think #___ matches letter ___ because ___.” “Do you think # ___ could match letter ___ because ____?” When You’re Done: • Raise your hand quietly and check with me. I will let you know how many you’ve got correct and if you can move on.

  18. Reflection Questions Work with your partner. Come up with a polished response to each question. Answer the following questions in complete sentences. Use proper vocabulary. Do not use the word “it”. The words in the word bank should be included in your answers. Select groups will present their answer to each question.

  19. Independent Practice / Homework • Complete Section 1 of the homework (evens only) in the back of your notebook. • Complete Section 2 on a separate sheet of paper. Choose one problem in each section and write a KWLR chart for each question.

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