2. SIMPLIFYING EXPESSIONS WITH EXPONENT PROPERTIES

3. Use the Exponent Express guide to follow along with the instruction. If you need a copy of the guide, click here to open and print it in Word. here Or, if you’d just like to practice, skip ahead to here and choose either easy, medium, or hard practice problems.here EXPONENT EXPRESS

4. For every nonzero number a, a 0 = 1 ZERO EXPONENT PROPERTY

5. For example, ======

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7. Answers ====

8. For every nonzero number a and integer n, a - n = NEGATIVE EXPONENT PROPERTY

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11. Answers ====

12. For every nonzero number a and integers m and n, = MULTIPLYING POWERS WITH THE SAME BASE

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15. Answers ====

16. For every nonzero number a and integers m and n, = RAISING A POWER TO A POWER PROPERTY

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19. Answers ====

20. For every nonzero number a and integers m and n, = DIVIDING POWERS WITH THE SAME BASE

21. For example, ======

22. Try it! ====

23. Answers ====

24. For every nonzero number a and integers m and n, = RAISING A QUOTIENT TO A POWER

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26. Try it! ====

27. Answers ====

28. Ready to practice? SIMPLIFYING WITH EXPONENTS PRACTICE Need some more help before practicing? SIMPLIFYING WITH EXPONENTS PRACTICE SHORT VIDEO CLIP TUTORIALS

29. SIMPLIFYING WITH EXPONENTS PRACTICE Easy Medium Hard Easy Medium Hard

30. Easy - Problem #1 = 101 Back to problem levels

31. In this problem, you forgot that any value to the zero power equals 1.

32. YOU GOT IT RIGHT! In this problem, you remembered that any value to the zero power equals 1.

33. Easy - Problem #2 =

34. In this problem, you only need to send the “x” to the denominator. The exponent only relates to the variable since there are not parentheses around the “6x.”

35. YOU GOT IT RIGHT! In this problem, you remembered that the exponent “-8” only relates to “x” so 6 should stay in the numerator.

36. Easy - Problem #3 =

37. In this problem, the exponents need to be added since two terms with the same base are being multiplied.

38. YOU GOT IT RIGHT! You remembered that the exponents need to be added since two terms with the same base are being multiplied.

39. Easy - Problem #4 =

40. In this problem, the exponents need to be multiplied since you are raising a power to a power.

41. YOU GOT IT RIGHT! You remembered that exponents need to be multiplied since you are raising a power to a power.

42. Easy - Problem #5 =

43. In this problem, both “8” and “y” both need to be squared since they are both in parentheses.

44. YOU GOT IT RIGHT! You remembered to square both the “8” and the “y” since they were both in the parentheses.

45. Easy - Problem #6 =

46. In this problem, the numerator and the denominator have the same base so the exponents should be subtracted. (numerator exponent minus denominator exponent)

47. YOU GOT IT RIGHT! You remembered to subtract the exponents since the numerator and the denominator had the same base.

48. Easy - Problem #7 =

49. In this problem, the numerator and the denominator have the same base so the exponents should be subtracted. (numerator exponent - denominator exponent)

50. YOU GOT IT RIGHT! You remembered to subtract the exponents since the numerator and the denominator had the same base. End Exponent ExpressContinue on to next level

51. Medium - Problem #1 =

52. In this problem, you need to remember that any value to the zero power equals 1.

53. YOU GOT IT RIGHT! You remembered that any value to the zero power equals 1. Since “y” to the zero power equals 1, you multiplied “5” times “x” times “1.”

54. Medium - Problem #2 =

55. In this problem, you need to remember that any value to the zero power equals 1.

56. YOU GOT IT RIGHT! You remembered that any value to the zero power equals 1.

57. Medium - Problem #3 =

58. In this problem, you need to remember that any value to the zero power equals 1.

59. YOU GOT IT RIGHT! You remembered that any value to the zero power equals 1. You also remembered that the “x” term should go to the denominator since its exponent is negative.

60. Medium - Problem #4 =

61. In this problem, you need to remember that a negative exponent will cause a term to move up or down. A term in the numerator will move to the denominator if it has a negative exponent.

62. YOU GOT IT RIGHT! You used the negative exponents properly. Negative exponents will cause a term to move up or down.

63. Medium - Problem #5 =

64. In this problem, you need to add exponents when multiplying terms with the same base.

65. YOU GOT IT RIGHT! You remembered to add exponents when multiplying terms that have the same base.

66. Medium - Problem #6 =

67. In this problem, you need to add exponents when multiplying terms with the same base.

68. YOU GOT IT RIGHT! You remembered to add exponents when multiplying terms that have the same base.

69. Medium - Problem #7 =

70. In this problem, you need to multiply exponents when raising a power to a power

71. YOU GOT IT RIGHT! You remembered to multiply exponents when raising a power to a power.

72. Medium - Problem #8 =

73. In this problem, there are two steps. First, multiply the exponents separated by parentheses (raise a power to a power). Then, since the two remaining terms have the same base, add the exponents.

74. YOU GOT IT RIGHT! You remembered to first multiply exponents the exponents separated by parentheses. Next, you added the two remaining exponents.

75. Medium - Problem #9 =

76. In this problem, you need to square everything inside the parentheses, then simplify.

77. YOU GOT IT RIGHT! You remembered to square everything inside of the parentheses.

78. Medium - Problem #10 =

79. In this problem, you need to cube everything inside the parentheses, then simplify.

80. YOU GOT IT RIGHT! You remembered to cube everything inside of the parentheses.

81. Medium - Problem #11 =

82. In this problem, you need to subtract the exponents because the numerator and the denominator have the same base.

83. YOU GOT IT RIGHT! You remembered to subtract the exponents because the numerator and the denominator had the same base.

84. Medium - Problem #12 =

85. In this problem, you need to subtract the exponents because the numerator and the denominator have the same base.

86. YOU GOT IT RIGHT! You remembered to subtract the exponents because the numerator and the denominator had the same base.

87. Medium - Problem #13 =

88. In this problem, you need to square the numerator and the denominator since the fraction is contained within the parentheses.

89. YOU GOT IT RIGHT! You remembered to square the numerator and the denominator since they were both in the parentheses.

90. Medium - Problem #14 =

91. In this problem, you need to apply the exponent to both the numerator and the denominator since the fraction is contained within the parentheses.

92. YOU GOT IT RIGHT! You remembered to apply the exponent to both the numerator and the denominator since they were both in the parentheses. Continue on to next levelEnd Exponent Express

93. Hard - Problem #1 =

94. In this problem, you need to remember that any value raised to the zero power equals 1. Also, if a value in the numerator is raised to a negative power, it should be moved to the denominator.

95. YOU GOT IT RIGHT! You applied the zero exponent and negative exponent properties correctly.

96. Hard - Problem #2 =

97. In this problem, you need to remember that any value raised to the zero power equals 1. Also, if a value in the numerator is raised to a negative power, it should be moved to the denominator.

98. YOU GOT IT RIGHT! You applied the zero exponent and negative exponent properties correctly.

99. Hard - Problem #3 =

100. In this problem, a value in the numerator is raised to a negative power so it should be moved to the denominator. Only the part being raised to a negative power should be moved.

101. YOU GOT IT RIGHT! You applied the negative exponent property correctly by moving only the “y” term to the denominator.

102. Hard - Problem #4 =

103. In this problem, you need to remember that any value raised to the zero power equals 1. Also, if a value in the numerator is raised to a negative power, it should be moved to the denominator, and vice versa.

104. YOU GOT IT RIGHT! You applied the zero and negative exponent properties correctly.

105. Hard - Problem #5 =

106. In this problem, you need to remember to add the exponents of only the terms with a common base.

107. YOU GOT IT RIGHT! You added the exponents of the terms that had a common base.

108. Hard - Problem #6 =

109. In this problem, you need to remember to add the exponents of only the terms with a common base.

110. YOU GOT IT RIGHT! You added the exponents of the terms that had a common base.

111. Hard - Problem #7 =

112. In this problem, you need to remember two steps. First, you needed to remember to multiply exponents separated by parentheses (raise a power to a power). Next, you needed to remember that any value raised to the zero power equals 1.

113. YOU GOT IT RIGHT! You added the exponents of the terms that had a common base.

114. Hard - Problem #8 =

115. In this problem, you needed to remember to multiply exponents separated by parentheses (raise a power to a power). You also needed to add the two remaining exponents.

116. YOU GOT IT RIGHT! You added the exponents of the terms that had a common base.

117. Hard - Problem #9 =

118. In this problem, you needed to remember to raise everything inside the parentheses to the given power.

119. YOU GOT IT RIGHT! You applied all of the exponent properties in the right order and simplified correctly. Way to go!

120. Hard - Problem #10 =

121. In this problem, you needed to remember to raise everything inside the parentheses to the given power.

122. YOU GOT IT RIGHT! You applied all of the exponent properties in the right order and simplified correctly. Way to go!

123. Hard - Problem #11 =

124. In this problem, you needed to remember to subtract exponents when the numerator and the denominator have the same base. Also, don’t forget to simplify the coefficient portion correctly.

125. YOU GOT IT RIGHT! You subtracted the exponents because the numerator and the denominator had and same base. You also simplified correctly.

126. Hard - Problem #12 =

127. In this problem, you needed to remember to subtract exponents when the numerator and the denominator have the same base.

128. YOU GOT IT RIGHT! You subtracted the exponents because the numerator and the denominator had and same base. You also simplified correctly.

129. Hard - Problem #13 =

130. In this problem, you needed to remember to raise everything inside the parentheses to the given power. Also, don’t forget to multiply when you raise a power to a power.

131. YOU GOT IT RIGHT! You correctly multiplied the exponents inside the parentheses with those outside of the parentheses.

132. Hard - Problem #14 =

133. In this problem, you needed to remember to raise everything inside the parentheses to the given power. Also, don’t forget to multiply when you raise a power to a power.

134. YOU GOT IT RIGHT! You correctly multiplied the exponents inside the parentheses with those outside of the parentheses. You even simplified correctly. Way to go! Return to problem levelsEnd Exponent Express

135. SHORT VIDEO CLIP TUTORIALS EXPONENT PROPERTRY REVIEW EXPONENT EXAMPLES EXPONENT PROPERTIES EXPONENT RULES Return to instructionGo to problem levels

136. YOU’VE SUCCESSFULLY COMPLETED THE EXPONENT EXPRESS! Return to problem levelsReturn to instruction