Chapter 2

Use the order of operations to simplify the quantities for the following problems. $$ \frac{6^{2}-1}{5}+\frac{4^{3}+(2)(3)}{10} $$

For the following problems, use the distributive property to expand the quantities. $$(a+6)(x+y)$$

Simplify the following problems using the commutative property of multiplication. You need not use the distributive property. $$ 16 a b 2 c $$

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. $$ \frac{e^{11}}{e^{11}} $$

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. $$ \left[\frac{x^{2}(y-1)^{3}}{(x+6)}\right]^{4} $$

Use the order of operations to simplify the quantities for the following problems. $$ \frac{5\left[8^{2}-9(6)\right]}{2^{5}-7}+\frac{7^{2}-4^{2}}{2^{4}-5} $$

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

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

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. $$ \left(x^{n} t^{2 m}\right)^{4} $$

Use the order of operations to simplify the quantities for the following problems. $$ \frac{(2+1)^{3}+2^{3}+1^{3}}{6^{2}}-\frac{15^{2}-[2(5)]^{2}}{5 \cdot 5^{2}} $$

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

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. $$ \frac{x^{0}}{x^{0}} $$

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. $$ \frac{\left(x^{n+2}\right)^{3}}{x^{2 n}} $$

Use the order of operations to simplify the quantities for the following problems. $$ \frac{6^{3}-2 \cdot 10^{2}}{2^{2}}+\frac{18\left(2^{3}+7^{2}\right)}{2(19)-3^{3}} $$

For the following problems, use the distributive property to expand the quantities. $$1(a+16)$$

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. $$ \frac{a^{0} b^{0}}{c^{0}} $$

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. $$ (x y)^{\Delta} $$

Use algebraic notation to write the statement "a number divided by eight, plus five, is equal to ten."

For the following problems, use the distributive property to expand the quantities. $$0.48(0.34 a+0.61)$$

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. $$ \frac{8 a^{4} b^{0}}{4 a^{3}} $$

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. $$ (2 a b)^{t} $$

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

For the following problems, use the distributive property to expand the quantities. $$21.5(16.2 a+3.8 b+0.7 c)$$

For the following problems, use the distributive property to expand the quantities.

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. $$ \frac{24 x^{4} y^{4} z^{0} w^{8}}{9 x y w^{7}} $$

Is every integer a whole 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. $$ t^{2}\left(y^{4}\right) $$

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. $$ \frac{10 m^{\Delta}}{5 m^{\text {t }}} $$

Use the commutative property of multiplication to write a number equal to the number \(y x\).

For the following problems, use the distributive property to expand the quantities. $$2 z_{t}\left(L_{m}+8 k\right)$$

For the following problems, use the distributive property to expand the expressions. $$ (8 m+5 n) 6 p $$

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

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. $$ \frac{4^{3} a^{\Delta} a^{\square}}{4 a^{V}} $$

Use the distributive property to expand \(3(x+6)\).

Find the value of \(4 \cdot 2+5(2 \cdot 4-6 \div 3)-2 \cdot 5\).

For the following problems, use the distributive property to expand the expressions. $$ 3 y(2 x+4 z+5 w) $$

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. $$ a^{4} b^{6}\left(\frac{a^{10} b^{16}}{a^{5} b^{7}}\right) $$

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. $$ \left(\frac{4 x^{\Delta}}{2 y^{\nabla}}\right)^{\square} $$

Is the statement \(3(5 \cdot 3-3 \cdot 5)+6 \cdot 2-3 \cdot 4<0\) true or false?

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

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. $$ 3 a^{2} b^{3}\left(\frac{14 a^{2} b^{5}}{2 b}\right) $$

Draw a number line that extends from -2 to 2 and place points at all integers between and including -2 and 3 .

For the following problems, use the distributive property to expand the expressions. $$ (x+y)(4 a+3 b) $$

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. $$ \frac{(x+3 y)^{11}(2 x-1)^{4}}{(x+3 y)^{3}(2 x-1)} $$

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

Replace the \(*\) with the appropriate relation symbol \((<,>) .-7 *-3\).

For the following problems, use the distributive property to expand the expressions. $$ 10 a_{z}\left(b_{z}+c\right) $$

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. $$ \frac{40 x^{5} z^{10}\left(z-x^{4}\right)^{12}(x+z)^{2}}{10 z^{7}\left(z-x^{4}\right)^{5}} $$

Use the distributive property to expand \(5 a(2 x+8)\).

What whole numbers can replace \(x\) so that the statement \(-2 \leq x<2\) is true?