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Exponents

Exponents. Exponent. 6³. Base. 6³ is read “ Six Cubed ” 6³ means 6 x 6 x 6 (repeated multiplication) 6³ = 216. Any base to the zero power, equals one. Example: Any base to the first power, equals itself. Example:. 2 0 = 1. 5 0 = 1. 4 1 = 4. 7 1 = 7.

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Exponents

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  1. Exponents

  2. Exponent 6³ Base

  3. 6³ is read “Six Cubed” 6³means6 x 6 x 6 (repeated multiplication) 6³ = 216

  4. Any base to the zero power, equals one. Example: • Any base to the first power, equals itself. Example: 20 = 1 50 = 1 41 = 4 71 = 7

  5. Evaluate Exponents • Evaluating Exponents:means to find the VALUE of. Example: • 3² = • -9º = • (-3)³ = 9 -1 -27

  6. Tricky Integer Bases = • Exponents tell you how many times to multiply the base Positive Base Negative Base Evaluate: Evaluate: 9 -9 ** Now check your answer with your calculators **

  7. What patterns do you notice?

  8. If you have a negative base and an odd exponent , the answer is negative. Example: Example: • If you have a negative base and an even exponent , the answer is positive. Example: Example: (-5)1 = -5 (-5)3 = -125 (-5)2 = 25 (-5)4 = 625

  9. 1 1 3 125 • 1 • 625 -9 100 16 1 -1 -7 -1

  10. Properties of Exponents • Complete the table in your notes and look for a pattern

  11. Rule 1: When multiplying two numbers with the same base,keep base and add the exponents. 3³ x 3² . x 3 x 3 x 3 x 3 x 3 3 x 3 x 3 3 x 3

  12. Properties of Exponents • Complete the table in your notes and look for a pattern

  13. Rule 2: When dividing two numbers with the same base,keep base and subtract the exponents. Why does x0 = 1?

  14. Rule 3 When raising a number with an exponent to a power,multiply the exponents. (3²)³ (3²) x (3²) x (3²) (3 x 3) x (3 x 3) x (3 x 3) 3 x 3 x 3 x3 x 3 x 3

  15. Negative Exponents • Negative Exponents are NOT negative numbers • Negative Exponents are greater than 0, but less than one • Negative Exponents can be written as fractions and decimals

  16. Example = = = = Negative Exponents Video

  17. Simplify

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