Chapter 2

Use the order of operations to simplify the following. $$ 3^{2}+4 \cdot 5 $$

Are all positive numbers greater than all negative numbers?

Use the order of operations to find each value. $$4+3[2+3(1+8 \div 4)]$$

For the following problems, simplify the expressions. $$ 48-3\left[\frac{1+17}{6}\right] $$

Perform each multiplication in one step. $$ x^{4} \cdot 4 y^{2} \cdot 2 x^{2} \cdot 7 y^{6} $$

Make use of either or both the power rule for products and the power rule for powers to simplify each expression. $$ \left[\left(12 c^{4} u^{3}(w-3)^{2}\right]^{5}\right. $$

Use the order of operations to simplify the following. $$ 2^{3}+3^{3}-8 \cdot 4 $$

Is 0 greater than all negative numbers?

Use the order of operations to find each value. $$\frac{19+2\\{5+2[18+6(4+1)]\\}}{5 \cdot 6-3(5)-2}$$

For the following problems, simplify the expressions. $$ 48-3\left[\frac{1+17}{6}\right] $$

Perform each multiplication in one step. $$ (x-y)^{3} \cdot 4(x-y)^{2} $$

Make use of either or both the power rule for products and the power rule for powers to simplify each expression. $$ \left[10 t^{4} y^{7} j^{3} d^{2} v^{6} n^{4} g^{8}(2-k)^{17}\right]^{4} $$

Use the order of operations to simplify the following. $$ 1^{4}+\left(2^{2}+4\right)^{2} \div 2^{3} $$

Fill in the ( ) to make each statement true. Use the associative properties. \([(7 m-2)(m+3)](m+4)=(7 m-2)[(\quad)(\quad)]\)

Is there a largest positive number? Is there a smallest negative number?

For the following problems, use the order of operations to find each value. $$2+3(6)$$

For the following problems, simplify the expressions. $$ \frac{29+11}{6-1} $$

Perform each multiplication in one step. $$ 8 x^{4} y^{2} x x^{3} y^{5} $$

Make use of either or both the power rule for products and the power rule for powers to simplify each expression. $$ \left(x^{3} x^{5} y^{2} y^{6}\right)^{9} $$

Use the order of operations to simplify the following. $$ \left[6\left(10-2^{3}\right)\right]^{2}-10^{2}-6^{2} $$

For the following problems, use the order of operations to find each value. $$18-7(8-3)$$

For the following problems, simplify the expressions. $$ \frac{\frac{88}{11}+\frac{99}{9}+1}{\frac{54}{9}-\frac{22}{11}} $$

Perform each multiplication in one step. $$ 2 a a a^{3}\left(a b^{2} a^{3}\right) b 6 a b^{2} $$

Make use of either or both the power rule for products and the power rule for powers to simplify each expression. $$ \left(10^{6} \cdot 10^{12} \cdot 10^{5}\right)^{10} $$

Use the order of operations to simplify the following. $$ \frac{5^{2}+6^{2}-10}{1+4^{2}}+\frac{0^{4}-0^{5}}{7^{2}-6 \cdot 2^{3}} $$

What whole numbers can replace \(x\) so that the following statement is true?

For the following problems, use the order of operations to find each value. $$8 \cdot 4 \div 16+5$$

For the following problems, simplify the expressions. $$ \frac{8 \cdot 6}{2}+\frac{9 \cdot 9}{3}-\frac{10 \cdot 4}{5} $$

Perform each multiplication in one step. $$ a^{n} \cdot a^{m} \cdot a^{r} $$

Make use of the power rule for quotients, the power rule for products, the power rule for powers, or a combination of these rules to simplify each expression. $$ \left(\frac{a}{c}\right)^{5} $$

For the following problems, write each of the quantities using exponential notation. \(b\) to the fourth

Draw a number line that extends from -5 to 3 and place points at all numbers greater than or equal to -4 but strictly less than 2 .

For the following problems, use the order of operations to find each value. $$(21+4) \div 5 \cdot 2$$

For the following problems, write the appropriate relation symbol \((=,<,>)\) in place of the \(*\). $$ 22 * 6 $$

Find each quotient $$ \frac{y^{9}}{y^{5}} $$

Make use of the power rule for quotients, the power rule for products, the power rule for powers, or a combination of these rules to simplify each expression. $$ \left(\frac{2 x}{3 y}\right)^{3} $$

For the following problems, write each of the quantities using exponential notation. \(a\) squared

What property of real numbers justifies \(a(b+c)=(b+c) a ?\)

For the following problems, next to each real number, note all collections to which it belongs by writing \(N\) for natural numbers, \(W\) for whole numbers, \(Z\) for integers, \(Q\) for rational numbers, Ir for irrational numbers, and \(R\) for real numbers. Some numbers may require more than one letter. $$\frac{1}{2}$$

For the following problems, use the order of operations to find each value. $$3(8+2) \div 6+3$$

For the following problems, write the appropriate relation symbol \((=,<,>)\) in place of the \(*\). $$ 9[4+3(8)] * 6[1+8(5)] $$

Find each quotient $$ \frac{a^{7}}{a} $$

Make use of the power rule for quotients, the power rule for products, the power rule for powers, or a combination of these rules to simplify each expression. $$ \left(\frac{x^{2} y^{4} z^{7}}{a^{5} b}\right)^{9} $$

For the following problems, write each of the quantities using exponential notation. \(x\) to the eighth

Use the distributive property to rewrite each of the following quantities. $$3(2+1)$$

For the following problems, use the order of operations to find each value. $$6(4+1) \div(16 \div 8)-15$$

For the following problems, write the appropriate relation symbol \((=,<,>)\) in place of the \(*\). $$ 3(1.06+2.11) * 4(11.01-9.06) $$

Find each quotient $$ \frac{(x+6)^{5}}{(x+6)^{3}} $$

Make use of the power rule for quotients, the power rule for products, the power rule for powers, or a combination of these rules to simplify each expression. $$ \left[\frac{2 a^{4}(b-1)}{3 b^{3}(c+6)}\right]^{4} $$

For the following problems, write each of the quantities using exponential notation. (-3) cubed