Chapter 2

Use the distributive property to rewrite each of the following quantities. $$(x+6) 7$$

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. $$0$$

For the following problems, use the order of operations to find each value. $$6(4-1)+8(3+7)-20$$

For the following problems, write the appropriate relation symbol \((=,<,>)\) in place of the \(*\). $$ 2 * 0 $$

Find each quotient $$ \frac{26 x^{4} y^{6} z^{2}}{13 x^{2} y^{2} z} $$

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. $$ \left(\frac{8 a^{3} b^{2} c^{6}}{4 a^{2} b}\right)^{3} $$

For the following problems, write each of the quantities using exponential notation. 5 times \(s\) squared

Use the distributive property to rewrite each of the following quantities. $$4(a+y)$$

For the following problems, use the order of operations to find each value. $$(8)(5)+2(14)+(1)$$

Find each value. Assume the base is not zero. $$ \frac{y^{7}}{y^{3}} $$

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. $$ \left[\frac{(9+w)^{2}}{(3+w)^{5}}\right]^{10} $$

For the following problems, write each of the quantities using exponential notation. 3 squared times \(y\) to the fifth

Use the distributive property to rewrite each of the following quantities. $$(9+2) a$$

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. $$86.3333 \ldots$$

For the following problems, use the order of operations to find each value. $$61-22+4[3(10)+11]$$

For the following problems, state whether the letters or symbols are the same or different. \(>\) and \(\not<\)

Find each value. Assume the base is not zero. $$ \frac{6 x^{4}}{2 x^{3}} $$

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. $$ \left[\frac{5 x^{4}(y+1)}{5 x^{4}(y+1)}\right]^{6} $$

For the following problems, write each of the quantities using exponential notation. \(a\) cubed minus \((b+7)\) squared

Use the distributive property to rewrite each of the following quantities. $$a(x+5)$$

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. $$49.125125125 \ldots$$

For the following problems, use the order of operations to find each value. $$\frac{(1+16-3)}{7}+5(12)$$

For the following problems, state whether the letters or symbols are the same or different. $$ a=b \text { and } b=a $$

Find each value. Assume the base is not zero. $$ \frac{14 a^{7}}{7 a^{2}} $$

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. $$ \left(\frac{16 x^{3} v^{4} c^{7}}{12 x^{2} v c^{6}}\right)^{0} $$

For the following problems, write each of the quantities using exponential notation. \((21-x)\) cubed plus \((x+5)\) to the seventh

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

For the following problems, use the order of operations to find each value. $$\frac{8(6+20)}{8}+\frac{3(6+16)}{22}$$

Find each value. Assume the base is not zero. $$ \frac{26 x^{2} y^{5}}{4 x y^{2}} $$

Use the power rules for exponents to simplify the following problems. Assume that all bases are nonzero and that all variable exponents are natural numbers. $$ (a c)^{5} $$

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

Use the commutative property of addition and multiplication to write expressions for an equal number for the following problems. You need not perform any calculations. $$x+3$$

For the following problems, draw a number line that extends from -3 to 3\. Locate each real number on the number line by placing a point (closed circle) at its approximate location. $$1 \frac{1}{2}$$

For the following problems, use the order of operations to find each value. $$18 \div 2+55$$

For the following problems, use algebraic notataion. 8 plus 9

Find each value. Assume the base is not zero. $$ \frac{36 a^{4} b^{3} c^{8}}{8 a b^{3} c^{6}} $$

Use the power rules for exponents to simplify the following problems. Assume that all bases are nonzero and that all variable exponents are natural numbers. $$ (n m)^{7} $$

For the following problems, write each of the quantities using exponential notation. \((21-x)\) cubed plus \((x+5)\) to the seventh

Use the commutative property of addition and multiplication to write expressions for an equal number for the following problems. You need not perform any calculations. $$5+y$$

For the following problems, draw a number line that extends from -3 to 3\. Locate each real number on the number line by placing a point (closed circle) at its approximate location. $$-2$$

For the following problems, use the order of operations to find each value. $$21 \div 7 \div 3$$

For the following problems, use algebraic notataion. 62 divided by \(f\)

Use the power rules for exponents to simplify the following problems. Assume that all bases are nonzero and that all variable exponents are natural numbers. $$ (2 a)^{3} $$

For the following problems, write each of the quantities using exponential notation. \(2 \cdot 3 \cdot 3 \cdot 3 \cdot 3 x x y y y y y\)

Use the commutative property of addition and multiplication to write expressions for an equal number for the following problems. You need not perform any calculations. $$10 x$$

For the following problems, draw a number line that extends from -3 to 3\. Locate each real number on the number line by placing a point (closed circle) at its approximate location. $$-\frac{1}{8}$$

For the following problems, use the order of operations to find each value. $$85 \div 5 \cdot 5-85$$

For the following problems, use algebraic notataion. 8 times \((x+4)\)

Find each value. Assume the base is not zero. $$ \frac{52 a^{7} b^{3}(a+b)^{8}}{26 a^{2} b(a+b)^{8}} $$

Use the power rules for exponents to simplify the following problems. Assume that all bases are nonzero and that all variable exponents are natural numbers. $$ (2 a)^{5} $$