Chapter 2

Use the order of operations to simplify the quantities for the following problems. $$ 3^{2}+7 $$

Simplify using the commutative property of multiplication for the following problems. You need not use the distributive property. $$\left(\frac{1}{2}\right) d\left(\frac{1}{4}\right) e\left(\frac{1}{2}\right) a$$

Is every rational number an integer?

For the following problems, rewrite each phrase using algebraic notation. \((a+b)\) divided by \((a+4)\)

The temperature today in Los Angeles was eighty-two degrees. Represent this temperature by real number.

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. $$ \frac{6^{4}}{6^{3}} $$

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. $$ \left(a b^{3} c^{2}\right)^{5}\left(a^{2} b^{2} c\right)^{2} $$

Use the order of operations to simplify the quantities for the following problems. $$ 4^{3}-18 $$

Can two rational numbers be added together to yield an integer? If so, give an example.

The temperature today in Marbelhead was six degrees below zero. Represent this temperature by real number.

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. $$ \frac{2^{9}}{2^{4}} $$

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. $$ \frac{\left(6 a^{2} b^{8}\right)^{2}}{\left(3 a b^{5}\right)^{2}} $$

Use the order of operations to simplify the quantities for the following problems. $$ 5^{2}+2(40) $$

Simplify using the commutative property of multiplication for the following problems. You need not use the distributive property. $$1(x+2 y)(6+z) 9(3 x+5 y)$$

For the following problems, on the number line, how many units (intervals) are there bet ween? 0 and \(2 ?\)

For the following problems, introduce a variable (any letter will do) and use appropriate algebraic symbols to write the given statement. Five times a number, minus one, equals zero.

On the number line, how many units between -3 and \(2 ?\)

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. $$ \frac{4^{16}}{4^{13}} $$

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

Use the order of operations to simplify the quantities for the following problems. $$ 8^{2}+3+5(2+7) $$

For the following problems, use the distributive property to expand the quantities. $$2(y+9)$$

For the following problems, on the number line, how many units (intervals) are there bet ween? -5 and \(0 ?\)

For the following problems, introduce a variable (any letter will do) and use appropriate algebraic symbols to write the given statement. A number divided by six is greater than or equal to forty-four.

On the number line, how many units between -4 and \(0 ?\)

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. $$ \frac{x^{5}}{x^{3}} $$

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. $$ \frac{\left(x^{6} y^{5}\right)^{3}}{\left(x^{2} y^{3}\right)^{5}} $$

Use the order of operations to simplify the quantities for the following problems. $$ 2^{5}+3(8+1) $$

For the following problems, use the distributive property to expand the quantities. $$b(r+5)$$

For the following problems, on the number line, how many units (intervals) are there bet ween? 0 and \(6 ?\)

For the following problems, introduce a variable (any letter will do) and use appropriate algebraic symbols to write the given statement. Sixteen minus twice a number equals five.

\(a+b=b+a\) is an illustration of the ____________ property of addition.

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. $$ \frac{y^{4}}{y^{3}} $$

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. $$ \frac{\left(a^{8} b^{10}\right)^{3}}{\left(a^{7} b^{5}\right)^{3}} $$

Use the order of operations to simplify the quantities for the following problems. $$ 3^{4}+2^{4}(1+5)^{3} $$

For the following problems, use the distributive property to expand the quantities. $$m(u+a)$$

For the following problems, on the number line, how many units (intervals) are there bet ween? -8 and \(0 ?\)

Determine whether the statements for the following problems are true or false. $$6-4(4)(1) \leq 10$$

\(s t=t s\) is an illustration of the ______________ property of ______________.

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. $$ \frac{y^{9}}{y^{4}} $$

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. $$ \frac{\left(m^{5} n^{6} p^{4}\right)^{4}}{\left(m^{4} n^{5} p\right)^{4}} $$

Use the order of operations to simplify the quantities for the following problems. $$ \left(6^{2}-4^{2}\right) \div 5 $$

For the following problems, use the distributive property to expand the quantities. $$k(j+1)$$

For the following problems, on the number line, how many units (intervals) are there bet ween? -3 and \(4 ?\)

Determine whether the statements for the following problems are true or false. $$5(4+2 \cdot 10) \geq 110$$

Use the commutative properties of addition and multiplication to write equivalent expressions for the following problems. $$ y+12 $$

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. $$ \frac{k^{16}}{k^{13}} $$

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. $$ \frac{\left(x^{8} y^{3} z^{2}\right)^{5}}{\left(x^{6} y z\right)^{6}} $$

Use the order of operations to simplify the quantities for the following problems. $$ 2^{2}\left(10-2^{3}\right) $$

For the following problems, use the distributive property to expand the quantities. $$x(2 y+5)$$

For the following problems, on the number line, how many units (intervals) are there bet ween? \(m\) and \(n, m>n ?\)