Chapter R3, Problem 89PE

For Exercises 69-96, simplify by using the order of operations. (See Examples 8-9.)

69. $5+3^3$

70. $10-2^4$

71. $5\cdot 2^3$

72. $12÷2^2$

73. ${(2+3)}^2$

74. ${(4-1)}^3$

75. $2^2+3^2$

76. $4^3-1^3$

77. $6+10÷2\cdot 3-4$

78. $12÷3\cdot 4-18$

79. $4^2-{(5-2)}^2\cdot 3$

80. $5-3{(8÷4)}^2$

81. $2-5{(9-4\sqrt{25})}^2$

82. $5^2-(\sqrt{9}+4÷2)$

83. ${\left(-\frac{3}{5}\right)}^2-\frac{3}{5}\cdot \frac{5}{9}+\frac{7}{10}$

84. $\frac{1}{2}-\left(\frac{2}{3}÷\frac{5}{9}\right)+\frac{5}{6}$

85. $1.75÷0.25-{(1.25)}^2$

86. $5.4-{(0.3)}^2÷0.09$

87. $\frac{\sqrt{{10}^2-8^2}}{3^2}$

88. $\frac{\sqrt{16-7}+3^2}{\sqrt{16}-\sqrt{4}}$

89. $-\left|-11+5\right|+\left|7-2\right|$

90. $-\left|-8-3\right|-(-8-3)$

91. $25-2\left[{(7-3)}^2÷4\right]+\sqrt{18-2}$

92. $\sqrt{29-2^2}+\left[8-3(6-2)\right]÷4\cdot 5$

93. $\frac{\left|(10-7)-2^3\right|}{6-16÷8\cdot 3}$

94. $\frac{\left|-12-{(7-3^2)}^2\right|}{40-6^2-8÷2}$

95. ${\left(\frac{1}{2}\right)}^2+{\left(\frac{6-4}{5}\right)}^2+{\left(\frac{5+2}{10}\right)}^2$

96. ${\left(\frac{2^3}{2^3+1}\right)}^2÷{\left[\frac{8-(-2)}{3^2}\right]}^2$

Example 8

Applying the Order of Operations

Simplify the expression. $10-{\left[2-4(6-8)\right]}^2+\sqrt{16-7}$

Example 9

Applying the Order of Operations Simplify the expression. $\frac{\left|{(-3)}^3+(5^2-3)\right|}{-15÷(-3)(2)}$