Chapter 2

Determine whether the statements for the following problems are true or false. $$8 \cdot 6-48 \leq 0$$

Use the commutative properties of addition and multiplication to write equivalent expressions for the following problems. $$ a+4 b $$

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

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. $$ \frac{\left(10 x^{4} y^{5} z^{11}\right)^{3}}{\left(x y^{2}\right)^{4}} $$

Use the order of operations to simplify the quantities for the following problems. $$ \left(3^{4}-4^{3}\right) \div 17 $$

For the following problems, use the distributive property to expand the quantities. $$z(x+9 w)$$

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

Determine whether the statements for the following problems are true or false. $$\frac{20+4.3}{16}<5$$

Use the commutative properties of addition and multiplication to write equivalent expressions for the following problems. $$ 6 x $$

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. $$ \frac{y^{5}}{y^{2}} $$

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. $$ \frac{\left(9 a^{4} b^{0}\right)\left(2 b^{2} e\right)}{\left(3 a^{3} b\right)(6 b c)} $$

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

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

Find the value of \(6+3(15-8)-4\).

Determine whether the statements for the following problems are true or false. $$2[6(1+4)-8]>3(11+6)$$

Use the commutative properties of addition and multiplication to write equivalent expressions for the following problems. $$ 2(a-1) $$

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. $$ \frac{m^{16}}{m^{9}} $$

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. $$ \frac{\left(2 x^{3} y^{3}\right)^{4}\left(5 x^{6} y^{8}\right)^{2}}{\left(4 x^{5} y^{3}\right)^{2}} $$

Use the order of operations to simplify the quantities for the following problems. $$ \left(2^{4}+2^{5}-2^{3} \cdot 5\right)^{2} \div 4^{2} $$

For the following problems, use the distributive property to expand the quantities. $$(8+2 f) g$$

Find the value of \(5(8-6)+3(5+2 \cdot 3)\).

Determine whether the statements for the following problems are true or false. $$6[4+8+3(26-15)] \neq 3[7(10-4)]$$

Use the commutative properties of addition and multiplication to write equivalent expressions for the following problems. $$ (-8)(4) $$

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. $$ \frac{a^{9} b^{6}}{a^{5} b^{2}} $$

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

Use the order of operations to simplify the quantities for the following problems. $$ 1^{6}+0^{8}+5^{2}(2+8)^{3} $$

For the following problems, use the distributive property to expand the quantities. $$c(2 a+10 b)$$

Are the statements \(y<4\) and \(y \geq 4\) the same or different?

The number of different ways 5 people can be arranged in a row is \(5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 .\) How many ways is this?

Use the commutative properties of addition and multiplication to write equivalent expressions for the following problems. $$ (6)(-9)(-2) $$

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. $$ \frac{y^{3} w^{10}}{y w^{5}} $$

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

Use the order of operations to simplify the quantities for the following problems. $$ (7)(16)-9^{2}+4\left(1^{1}+3^{2}\right) $$

For the following problems, use the distributive property to expand the quantities. $$15 x(2 y+3 z)$$

Use algebraic notation to write the statement "six times a number is less than or equal to eleven."

A box contains 10 computer chips. Three chips are to be chosen at random. The number of ways this can be done is $$\frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{3 \cdot 2 \cdot 1 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}$$

Use the commutative properties of addition and multiplication to write equivalent expressions for the following problems. $$ (x+y)(x-y) $$

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. $$ \frac{m^{17} n^{12}}{m^{16} n^{10}} $$

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

Use the order of operations to simplify the quantities for the following problems. $$ \frac{2^{3}-7}{5^{2}} $$

For the following problems, use the distributive property to expand the quantities. $$8 y(12 a+b)$$

The probability of obtaining four of a kind in a five-card poker hand is $$\frac{13 \cdot 48}{(52 \cdot 51 \cdot 50 \cdot 49 \cdot 48) \div(5 \cdot 4 \cdot 3 \cdot 2 \cdot 1)}$$ What is this probability?

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. $$ \frac{x^{5} y^{7}}{x^{3} y^{4}} $$

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

Use the order of operations to simplify the quantities for the following problems. $$ \frac{(1+6)^{2}+2}{19} $$

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

Three people are on an elevator in a five story building. If each person randomly selects a floor on which to get off, the probability that at least two people get off on the same floor is $$1-\frac{5 \cdot 4 \cdot 3}{5 \cdot 5 \cdot 5}$$ What is this probability?

Simplify the following problems using the commutative property of multiplication. You need not use the distributive property. $$ 8 x 3 y $$

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. $$ \frac{15 x^{20} y^{24} z^{4}}{5 x^{19} y z} $$

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. $$ \left(\frac{4^{2} a^{3} b^{7}}{b^{5} c^{4}}\right)^{2} $$