Chapter 2

For the following problems, write each of the quantities using exponential notation. $$ (2 y)(2 y) 2 y 2 y $$

For the pairs of real numbers shown in the following problems, write the appropriate relation symbol \((<,>,=)\) in place of the \(*\) $$-3 * 0$$

For the following problems, use the order of operations to find each value. $$\left(\frac{5}{12}-\frac{1}{4}\right)+\left(\frac{1}{6}+\frac{2}{3}\right)$$

For the following problems, locate the numbers on a number line by placing a point at their (approximate) position. $$ -1 \frac{3}{8} $$

Use the product rule and quotient rule of exponents to simplify the following problems. Assume that all bases are nonzero and that all exponents are whole numbers. $$ x^{2} x^{3} $$

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. $$ \left(10 a^{2} b\right)^{2} $$

For the following problems, write each of the quantities using exponential notation. $$ 3 x y x x y-(x+1)(x+1)(x+1) $$

For the following problems, use the order of operations to find each value. $$4\left(\frac{3}{5}-\frac{8}{15}\right)+9\left(\frac{1}{3}+\frac{1}{4}\right)$$

For the following problems, locate the numbers on a number line by placing a point at their (approximate) position. $$ 0 $$

Use the product rule and quotient rule of exponents to simplify the following problems. Assume that all bases are nonzero and that all exponents are whole numbers. $$ a^{9} a^{7} $$

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. $$ \left(8 x^{2} y^{3}\right)^{2} $$

For the following problems, expand the quantities so that no exponents appear. $$ 4^{3} $$

For the pairs of real numbers shown in the following problems, write the appropriate relation symbol \((<,>,=)\) in place of the \(*\) $$6 *-1$$

For the following problems, use the order of operations to find each value. $$\frac{0}{5}+\frac{0}{1}+0[2+4(0)]$$

For the following problems, locate the numbers on a number line by placing a point at their (approximate) position. $$ -4 \frac{1}{2} $$

Use the product rule and quotient rule of exponents to simplify the following problems. Assume that all bases are nonzero and that all exponents are whole numbers. $$ y^{5} y^{7} $$

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. $$ \left(x^{2} y^{3} z^{5}\right)^{4} $$

For the following problems, expand the quantities so that no exponents appear. $$ 6^{2} $$

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. $$5(6 h+1)$$

For the pairs of real numbers shown in the following problems, write the appropriate relation symbol \((<,>,=)\) in place of the \(*\) $$-\frac{1}{4} *-\frac{3}{4}$$

For the following problems, use the order of operations to find each value. $$0 \cdot 9+4 \cdot 0 \div 7+0[2(2-2)]$$

Draw a number line that extends from 10 to 20 . Place a point at all odd integers.

Use the product rule and quotient rule of exponents to simplify the following problems. Assume that all bases are nonzero and that all exponents are whole numbers. $$ m^{10} m^{2} $$

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. $$ \left(2 a^{5} b^{11}\right)^{0} $$

For the following problems, expand the quantities so that no exponents appear. $$ 7^{3} y^{2} $$

Draw a number line that extends from -10 to \(10 .\) Place a point at all negative odd integers and at all even positive integers.

Use the product rule and quotient rule of exponents to simplify the following problems. Assume that all bases are nonzero and that all exponents are whole numbers. $$ k^{8} k^{3} $$

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. $$ \left(x^{3} y^{2} z^{4}\right)^{5} $$

For the following problems, expand the quantities so that no exponents appear. $$ 8 x^{3} y^{2} $$

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. $$k(10 a-b)$$

Draw a number line that extends from -5 to \(10 .\) Place a point at all integers that are greater then or equal to -2 but strictly less than 5 .

Use the product rule and quotient rule of exponents to simplify the following problems. Assume that all bases are nonzero and that all exponents are whole numbers. $$ y^{3} y^{4} y^{6} $$

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. $$ \left(m^{6} n^{2} p^{5}\right)^{5} $$

For the following problems, expand the quantities so that no exponents appear. $$ \left(18 x^{2} y^{4}\right)^{2} $$

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. $$(21 c)(0.008)$$

For the following problems, state whether the given statements are the same or different. $$x=y \text { and } y=x$$

Draw a number line that extends from -10 to \(10 .\) Place a point at all real numbers that are strictly greater than -8 but less than or equal to 7 .

Use the product rule and quotient rule of exponents to simplify the following problems. Assume that all bases are nonzero and that all exponents are whole numbers. $$ 3 x^{2} \cdot 2 x^{5} $$

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. $$ \left(a^{4} b^{7} c^{6} d^{8}\right)^{8} $$

For the following problems, expand the quantities so that no exponents appear. $$ \left(9 a^{3} b^{2}\right)^{3} $$

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. $$(-16)(4)$$

Is there a smallest integer? If so, what is it?

For the following problems, state whether the given statements are the same or different. Represent the product of 3 and \(x\) five different ways.

Use the product rule and quotient rule of exponents to simplify the following problems. Assume that all bases are nonzero and that all exponents are whole numbers. $$ a^{2} a^{3} a^{8} $$

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. $$ \left(x^{2} y^{3} z^{9} w^{7}\right)^{3} $$

For the following problems, expand the quantities so that no exponents appear. $$ 5 x^{2}\left(2 y^{3}\right)^{3} $$

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. $$(5)(b-6)$$

Is there a smallest whole number? If so, what is it?

For the following problems, state whether the given statements are the same or different. Represent the sum of \(a\) and \(b\) two different ways.

For the following problems, write the appropriate relation symbol \((=,<,>)\). $$ \begin{array}{ll} -3 & 0 \end{array} $$