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EXPONENTS

EXPONENTS. EXPONENTIAL NOTATION. 2 IS THE EXPONENT OR POWER. X IS THE BASE. EXPONENTIAL NOTATION. THE BASE IS SQUARED. EXPONENTIAL NOTATION. EXPONENT IS THE NUMBER OF TIMES THE BASE IS MULTIPLIED BY ITSELF. EXPONENTIAL NOTATION. 8 IS THE EXPONENT. Y IS THE BASE. EXPONENTIAL NOTATION.

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EXPONENTS

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  1. EXPONENTS

  2. EXPONENTIAL NOTATION 2 IS THE EXPONENT OR POWER X IS THE BASE

  3. EXPONENTIAL NOTATION THE BASE IS SQUARED

  4. EXPONENTIAL NOTATION EXPONENT IS THE NUMBER OF TIMES THE BASE IS MULTIPLIED BY ITSELF

  5. EXPONENTIAL NOTATION 8 IS THE EXPONENT Y IS THE BASE

  6. EXPONENTIAL NOTATION 8 IS THE EXPONENT Y IS THE BASE

  7. Compare these two cases -6 IS THE BASE 6 IS THE BASE (THE NEG. SIGN IS NOT PART OF THE BASE, IT MUST REMAIN PART OF THE ANSWER)

  8. EXPONENTIAL NOTATION WHAT IS THE BASE? WHAT WILL BE SQUARED?

  9. EXPONENTIAL NOTATION WHAT IS THE BASE? -h is the base

  10. EXPONENTIAL NOTATION WHAT IS THE BASE? What will be raised to the 5th power?

  11. EXPONENTIAL NOTATION WHAT IS THE BASE? r will be raised to the 5th power

  12. TRY THESE

  13. TRY THESE

  14. EVALUATING EXPRESSIONS WITH EXPONENTS

  15. Evaluating Expression with Exponents Evaluate 2x2(x+y) When x=6 & y=3

  16. Evaluating Expression with Exponents Evaluate 2x2(x+y) When x=6 & y=3 Put in x & y values 2x2(x+y) = 2(6)2(6+3)

  17. Evaluating Expression with Exponents Evaluate 2x2(x+y) When x=6 & y=3 Put in x & y values Use PEMDAS 2x2(x+y) = 2(6)2(6+3) = 2(6)2(9) = 2(36)9 = 72•9 = 648

  18. MULTIPLYING SIMILAR BASES X2 X X

  19. MULTIPLYING SIMILAR BASES THE RULE IS TO ADD THE EXPONENTS

  20. MULTIPLYING SIMILAR BASES

  21. MULTIPLYING SIMILAR BASES

  22. TRY THESE PROBLEMS

  23. DIVIDING SIMILAR BASES

  24. DIVIDING SIMILAR BASES THE RULE IS TO SUBTRACT THE EXPONENT OF THE DENOMINATOR FROM THE EXPONENT OF THE NUMERATOR

  25. DIVIDING SIMILAR BASES THE RULE IS TO SUBTRACT THE EXPONENTS

  26. TRY THESE

  27. TRY THESE

  28. NEGATIVE EXPONENTS You can change a negative exponent to positive by switching it’s base from numerator to denominator or vice versa.

  29. NEGATIVE EXPONENTS MOVE THE BASE & EXPONENT FROM THE NUMERATOR TO THE DENOMINATOR OR VICE VERSA AND CHANGE THE SIGN OF THE EXPONENT

  30. NEGATIVE EXPONENTS X2/X2 IS WHAT PROPERTY?

  31. NEGATIVE EXPONENTS MULTIPLY NUMERATORS & MULTIPLY DENOMINATORS

  32. NEGATIVE EXPONENTS ANYTHING TO THE ZERO POWER IS EQUAL TO ?

  33. Why is anything to the zero power equal to 1?

  34. Check Out These Patterns

  35. Or For Anything

  36. SWITCHING A NEGATIVE EXPONENT CHANGES ITS SIGN THIS IS WHY

  37. Let’s compare the Neg. ExponentRule with the Dividing Fraction Rule To divide fractions you INVERT THE 2ND FRACTION AND CHANGE THE DIVISION SIGN TO MULTIPICATION For negative exponents you INVERT THE BASE WITH AND CHANGE THE SIGN OF THE EXPONENT

  38. Try These

  39. Try These

  40. What if the negative exponent is in the denominator? The same rule of inverting the base with the exponent and making the exponent positive applies but let see why this is so.

  41. What if the negative exponent is in the denominator? Use the Multiplicative Identity to Simplify

  42. What if the negative exponent is in the denominator? Do you remember what x0 is equal to?

  43. What if the negative exponent is in the denominator? INVERT AND CHANGE EXPONENT SIGN

  44. Try These

  45. Try These ANSWERS

  46. SUMMARY SO FAR INVERTING A NEGATIVE EXPONENT CHANGES ITS SIGN DIVIDING EXPONENTS SUBTRACT THE EXPONENT OF THE DENOMINATOR FROM THE EXPONENT OF THE NUMERATOR MULTIPLYING EXPONENTS ADD THE EXPONENTS

  47. DON’T BE MARY TO THE Z POWER GET WITH IT!

  48. POWER TO A POWER THIS IS A POWERFUL IDEA

  49. POWER TO A POWER VS. MULT. SIMILAR BASES MULTIPLY SIMILAR BASE PWR TO A PWR

  50. POWER TO A POWER MULTIPLY THE EXPONENTS

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