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8th Grade Slides

Learn to calculate values with positive and negative exponents, understand exponent rules, work on decimals and fractions, tackle odd and even exponents, and comprehend the product law of exponents with step-by-step examples. Master exponents with this comprehensive guide.

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8th Grade Slides

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  1. 8th Grade Slides Exponents

  2. Exponents • Key Skill: Calculate values of expressions with positive and negative exponents.

  3. Quick Review Exponent Base

  4. Exponent Review • Repeated multiplication:

  5. Exponent Review • Any number to the first power is?

  6. Exponent Review • Any number to the first power is itself • So • And

  7. Exponent Review • Any non-zero number to the power of 0 is?

  8. Exponent Review • Any non-zero number to the power of 0 is 1. • So, • and (assuming x does not = 0),

  9. Question • What is

  10. Question • What is • Is it the same as

  11. Odd and Even Exponents • Will a negative number raised to a power always be positive?

  12. Odd and Even Exponents • How do we know whether a negative number raised to a particular power will be positive or negative?

  13. Odd and Even Exponents • How do we know whether a negative number raised to a particular power will be positive or negative? Negative base with an odd exponent results in a NEGATIVE answer Negative base with an even exponent results in a POSITIVE answer

  14. Decimals and Fractions • Is this the same as

  15. Decimals and Fractions • Is this the same as No!

  16. Negative Exponents • Look at this progression of numbers: 33 = 32 = 31 = 30 = 3-1 = 3-2 = 3-3 =

  17. Negative Exponents • Look at this progression of numbers: 33 = 27 32 = 9 31 = 3 30 = 1 3-1 = 1/3 3-2 = 1/9 3-3 = 1/27

  18. Negative Exponents • Rule:

  19. Negative Exponents • The reverse is also true:

  20. Negative Exponents • We generally do NOT want negative exponents in our answer (unless we are using Scientific Notation). • We move bases with negative exponents to the denominator where they will turn positive. • If a negative exponent is found in a denominator, we move it to the numerator.

  21. Method Step 1: Take the RECIPROCAL of the base. What does RECIPROCAL MEAN? Step 2: The exponent moves with the base, but the negative sign in the exponent disappears.

  22. Examples

  23. Examples

  24. Exception • Numbers generally get LARGER when we square them. What kind of numbers get SMALLER when we square them?

  25. Exception • Numbers generally get LARGER when we square them. What kind of numbers get SMALLER when we square them? • Numbers between 0 and 1 (fractions and decimals)

  26. Classwork • Pages

  27. Exponent Laws • Key Skill: Apply the Laws of Exponents to simplify expressions.

  28. Exponents • Reminders: • Anything raised to the power of 1 is itself. • Any non-zero number raised to the power of 0 is 1. • When we see we use PEMDAS to determine what to do first. • In this case, raise ‘x’ to the 3rd power, THEN multiply by 4

  29. PEMDAS Parentheses ( ) Exponents 3 Multiplication x, Division ÷ Addition + Subtraction __

  30. Please Excuse My Dear Aunt Sally • Parentheses ( ) • Exponents 3 • Multiplication x, • Division ÷ • Addition + • Subtraction __

  31. Product Law of Exponents • How would we multiply:

  32. Product Law of Exponents • How would we multiply: • We could rewrite it as: (4 x 4 x 4) x (4 x 4)

  33. Product Law of Exponents • How would we multiply: • We could rewrite it as: (4 x 4 x 4) x (4 x 4) • Or with an exponent: • Note that we did NOT multiply the exponents, we ADDED them!

  34. Another Example • How would we multiply:

  35. Another Example • How would we multiply: • We would rewrite the equation as: • Or more simply as: 32 • Again, we ADDED the exponents

  36. Example with a variable • What is:

  37. Example with a variable • What is: • Rewrite as: • Or more simply as:

  38. Product Law of Exponents

  39. Contra-Example • Does the Product Law of Exponents apply here?

  40. Contra-Example • Does the Product Law of Exponents apply here? • No! We do NOT have a common base or a common exponent.

  41. Product Law of Exponents • What about:

  42. Product Law of Exponents • What about: • Does it matter what order we write the factors?

  43. Product Law of Exponents • What about: • Does it matter what order we write the factors? • How about:

  44. Product Law of Exponents • What about: • Does it matter what order we write the factors? • How about:

  45. More Examples

  46. More Examples

  47. The Other Product Law • How would we work with: • What’s different/what’s the same?

  48. The Other Product Law • How would we work with: • We can rewrite as: (4 x 4) x (3 x 3) • Or as (4 x 3) x (4 x 3) because order doesn’t matter when we multiply

  49. The Other Product Law • How would we work with: • We can rewrite as: (4 x 4) x (3 x 3) • Or as (4 x 3) x (4 x 3) because order doesn’t matter when we multiply • Now we can rewrite as

  50. The Other Product Law • How would we work with: • What’s different/what’s the same?

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