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Lesson 105 & 106

Lesson 105 & 106. Lessons 97 – 104 Review Evaluating Powers of Negative Bases Roots of Negative Numbers Negative Exponents Zero Exponents. Lesson 97 Example. If 2x + 4 = 6, what is the value of 3x – 7?. Lesson 98 Example. What is the measure of angle ABC and angle DEF?.

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Lesson 105 & 106

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  1. Lesson 105 & 106 Lessons 97 – 104 Review Evaluating Powers of Negative Bases Roots of Negative Numbers Negative Exponents Zero Exponents

  2. Lesson 97 Example • If 2x + 4 = 6, what is the value of 3x – 7?

  3. Lesson 98 Example • What is the measure of angle ABC and angle DEF?

  4. Lesson 99 Example • Simplify: -22 - (-2)2 - (-2)3

  5. Lesson 100 Example • The ratio of nuts to bolts was 11 to 2. If there were 260 nuts and bolts total in the pile, how many were bolts?

  6. Lesson 101 Example • Simplify: a a2 m m5 a4 m6

  7. Lesson 102 Example • Simplify by adding like terms: xxx + 3x2x + 4x3 + 2xy – 3yx

  8. Lesson 103 Example • Simplify: x (y – x – 4)

  9. Lesson 104 Example • Find the missing angle and classify the triangle by angles.

  10. Evaluating Powers • if the negative is inside parenthesis, it stays inside (-3)2 • if the negative is in front of the parenthesis or in front of the number (if no parenthesis), it stays in front -32

  11. Example 105.1 • Evaluate: • (-3)2 • -32

  12. Example 105.2 • Evaluate if a = -4: • a2 • -a2

  13. Example 105.3 • Evaluate if a = -2 and b = -3 • a2 – ab2 – b2

  14. Roots of Negative Numbers • Even Roots (square roots, fourth roots) • of a positive number is a positive number • of a negative number you won’t have to do • Odd Roots (third roots, fifth roots) • of a positive number is a positive number • of a negative number is a negative number

  15. Example 106.1 • Find:

  16. Example 106.2 • Find:

  17. Negative Exponents • negative exponents make reciprocals • if there’s a negative exponent on “top”, you move it to the bottom and make the exponent positive • if there’s a negative exponent on bottom, you move it to the top and make the exponent positive • you’ll hear me say “it’s negative, so flip it!”

  18. Example 106.3 • Simplify:

  19. Example 106.4 • Simplify:

  20. Example 106.5 • Simplify:

  21. Zero Exponents • ANYTHING raised to a zero power is equal to ONE!!

  22. Example 106.6 • simplify: • 20 • -20 • (-2)0

  23. Example 106.7 • Simplify: x2 y5 y-2 x-2

  24. Practice Problems • P.S. 106 • 2, 14-20, 22-30

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