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Properties of Exponents

Properties of Exponents. Algebra 2. Relax, you aren’t in any trouble. This exponent stuff is a piece of cake.

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Properties of Exponents

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  1. Properties of Exponents Algebra 2

  2. Relax, you aren’t in any trouble. This exponent stuff is a piece of cake. In this activity you will be maneuvering your way through every exponent property. In order to advance through the lesson, you must select the right responses and move ahead to the next property. If you make a mistake, you will be guided back to the property to try again. Upon completing every lesson, you will be required to take a 10 question quiz. Be sure of your answers though, one slip and you are sent back to the properties and have to start all over!

  3. TheProperties Product of Powers Power of a Product Quotient of Powers Zero Exponent Negative Exponents Power of a Quotient Power of a Power TheQuiz

  4. Product of Powers • When multiplying like bases, we have to ADD their exponents xm • xn= xm+n Example: x3 • x4 = x7 Now you choose the correct answer… x5 • x6 = ? x30 x56 x11

  5. Sorry! Try Again! Remember, if you are multiplying like bases, we do NOT multiply the exponents

  6. Notice if we were to break up the previous problem as the following… x5 • x6 = ? x • x • x • x • x • x • x • x • x • x • x Since x5 means x times itself five times and x6 means x times itself six times. How many of the x times itself did we end up with?

  7. Return to The Properties

  8. Notice if we were to break up the previous problem as the following… x5 • x6 = ? x • x • x • x • x • x • x • x • x • x • x Since x5 means x times itself five times and x6 means x times itself six times. How many of the x times itself did we end up with?

  9. Power of a Power • When a base with a power is raised to another power, we MULTIPLY their exponents (xm)n = xm • n Example: (x2)8 = x16 Now you choose the correct answer… (x3)4 = ? x12 x34 x7

  10. Sorry! Try Again! Remember, if you have a power to a power, we do NOT add the exponents

  11. Now if we were to break up the previous problem as the following… (x3)4 = ? (x • x • x)4 And continued to break these up using the ideas from the first property, we could get… (x • x • x) • (x • x • x) • (x • x • x) • (x • x • x) How many of the x times itself did we end up with?

  12. Return to The Properties

  13. Now if we were to break up the previous problem as the following… (x3)4 = ? (x • x • x)4 And continued to break these up using the ideas from the first property, we could get… (x • x • x) • (x • x • x) • (x • x • x) • (x • x • x) How many of the x times itself did we end up with?

  14. Power of a Product • When a product is raised to a power, EVERYTHING in the product receives that power (xy)m = xm • ym Example: (xy)7 = x7• y7 Now you choose the correct answer… (xy)2 = ? x2y x2y2 xy2

  15. Sorry! Try Again! Remember, if you have a product to a power, ALL terms must receive that power

  16. Now if we were to break up the previous problem as the following… (xy)2 = ? (xy) • (xy) And thinking about what happens when we multiply like bases, what would the powers of each variable be?

  17. Return to The Properties

  18. Now if we were to break up the previous problem as the following… (xy)2 = ? (xy) • (xy) And thinking about what happens when we multiply like bases, what would the powers of each variable be?

  19. Quotient of Powers • When dividing like bases, we have to SUBTRACT their exponents = xm-n Example: = x6 Now you choose the correct answer… = ? x8 x2 x24

  20. Sorry! Try Again! Remember, if you are dividing like bases, do NOT divide their exponents

  21. Now if we were to break up the previous problem as the following… Looking at the x’s in the numerator and the denominator. If every x in the numerator was cancelled by one in the denominator, how many of the x times themselves would be left and where would they be?

  22. Return to The Properties

  23. Now if we were to break up the previous problem as the following… Looking at the x’s in the numerator and the denominator. If every x in the numerator was cancelled by one in the denominator, how many of the x times themselves would be left and where would they be?

  24. Power of a Quotient • When a quotient is raised to a power, EVERYTHING in the quotient gets that power = Example: = Now you choose the correct answer… = ?

  25. Sorry! Try Again! Remember, if you have a quotient to a power, ALL terms receive that power

  26. Now if we were to break up the previous problem as the following… Looking at the x’s being multiplied in the numerator and the y’s being multiplied in the denominator, how many of the x times themselves are in the numerator and how many of the y times themselves are in the denominator?

  27. Return to The Properties

  28. Now if we were to break up the previous problem as the following… Looking at the x’s being multiplied in the numerator and the y’s being multiplied in the denominator, how many of the x times themselves are in the numerator and how many of the y times themselves are in the denominator?

  29. Zero Exponent • Anything to the power of zero is ALWAYS equal to one x0 = 1 Example: (4xy)0 = 1 Now you choose the correct answer… (9x5yz17)0 = ? 1 0 x

  30. Sorry! Try Again! Remember, if anything has zero as an exponent, that does NOT mean it equals zero Return to last slide

  31. Return to The Properties

  32. But Why? For a brief look at why anything to the power of zero is one, take a look at a few explanations here. x0 1

  33. Negative Exponents • We can never have a negative exponent, so if we have one we have to MOVE the base to make it positive. If it is on top it goes to the bottom, if it is on bottom it goes to the top. x-m = or = xm Example: = x4 Now you choose the correct answer… x-3 -x3

  34. Sorry! Try Again! Make sure to move the variable and make the exponent POSITIVE Return to last slide

  35. Return to The Properties Take The Quiz

  36. Simplify the following quiz questions using the properties of exponents that you have learned in the activity. Question #1: y4 • y5 = ? y20 y9 y45

  37. Sorry! Try Again! Time to head back and review the property Return to the property

  38. Return to The Properties

  39. Question #2: (d6)3 = ? d63 d9 d18

  40. Sorry! Try Again! Time to head back and review the property Return to the property

  41. Return to The Properties

  42. Question #3: (ab)5 = ? a5b5 ab5 a5b

  43. Sorry! Try Again! Time to head back and review the property Return to the property

  44. Return to The Properties

  45. Question #4: = ? x2 x4 x32

  46. Sorry! Try Again! Time to head back and review the property Return to the property

  47. Return to The Properties

  48. Question #5: = ?

  49. Sorry! Try Again! Time to head back and review the property Return to the property

  50. Return to The Properties

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