Chapter 1

Indicate whether the statement is true or false. Every integer is a rational number.

Evaluate the expression. $$ (-2 x)^{3}(-2 x)^{2} $$

Solve the equation by factoring, if required: $$ 4 x^{2}-9=0 $$

perform the indicated operations and simplify. \(\frac{6 x^{3}}{32} \cdot \frac{8}{3 x^{2}}\)

Find the values of \(x\) that satisfy the inequalities. $$ -4 x \geq 20 $$

Rewrite the number without radicals or exponents.. $$ \left(\frac{4}{9}\right)^{1 / 2} $$

Solve the given equation. $$ \frac{3}{5}(k+1)=\frac{1}{4}(2 k+3) $$

Rewrite the number without using exponents. $$ \left(a b^{2}\right)^{0}, \text { where } a, b \neq 0 $$

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ x^{2}-x y-6 y^{2} $$

Indicate whether the statement is true or false. Every natural number is an integer.

Perform the indicated operations and simplify. $$ (2 x+3)+(4 x-6) $$

Solve the equation by factoring, if required: $$ 8 m^{2}+64 m=0 $$

Perform the indicated operations and simplify. \(\frac{25 y^{4}}{12 y} \cdot \frac{3 y^{2}}{5 y^{3}}\)

Find the values of \(x\) that satisfy the inequalities. $$ -12 \leq-3 x $$

Rewrite the number without radicals or exponents.. $$ \left(\frac{9}{25}\right)^{3 / 2} $$

Solve the given equation. $$ 3\left(\frac{3 m}{4}-1\right)+\frac{m}{5}=\frac{42-m}{4} $$

Rewrite the number without using exponents. $$ \left(3 x^{2} y^{3}\right)^{0}, \text { where } x, y \neq 0 $$

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ 2 u^{2}+5 u v-12 v^{2} $$

Perform the indicated operations and simplify. $$ (-3 x+2)-(4 x-3) $$

Indicate whether the statement is true or false. Every rational number is a real number.

Perform the indicated operations and simplify. \(\frac{3 x^{3}}{8 x^{2}} \div \frac{15 x^{4}}{16 x^{5}}\)

Solve the equation by factoring, if required: $$ z(2 z+1)=6 $$

Find the values of \(x\) that satisfy the inequalities. $$ -6

Rewrite the number without radicals or exponents.. $$ \left(\frac{27}{8}\right)^{2 / 3} $$

Solve the given equation. $$ \frac{2 x-1}{3}+\frac{3 x+4}{4}=\frac{7(x+3)}{10} $$

Rewrite the number without using exponents. $$ \frac{2^{3} \cdot 2^{5}}{2^{4} \cdot 2^{9}} $$

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ x^{2}-3 x-1 $$

Perform the indicated operations and simplify. $$ \left(7 x^{2}-2 x+5\right)+\left(2 x^{2}+5 x-4\right) $$

Perform the indicated operations and simplify. \(\frac{6 x^{5}}{21 x^{2}} \div \frac{4 x}{7 x^{3}}\)

Solve the equation by factoring, if required: $$ 13 m=-5-6 m^{2} $$

Find the values of \(x\) that satisfy the inequalities. $$ 0 \leq x+1 \leq 4 $$

Rewrite the number without radicals or exponents.. $$ \left(-\frac{8}{125}\right)^{1 / 3} $$

Solve the given equation. $$ \frac{w-1}{3}+\frac{w+1}{4}=-\frac{w+1}{6} $$

Rewrite the number without using exponents. $$ \frac{6 \cdot 10^{4}}{3 \cdot 10^{2}} $$

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ m^{2}+2 m+3 $$

Perform the indicated operations and simplify. $$ \left(3 x^{2}+5 x y+2 y\right)+\left(4-3 x y-2 x^{2}\right) $$

Indicate whether the statement is true or false. $$ \text { Every irrational number is a real number. } $$

Solve the equation by completing the square. $$ x^{2}+2 x-8=0 $$

Perform the indicated operations and simplify. \(\frac{3 x}{x+2 y} \cdot \frac{5 x+10 y}{6}\)

Find the values of \(x\) that satisfy the inequalities. $$ x+1>4 \text { or } x+2<-1 $$

Rewrite the number without radicals or exponents.. $$ 8^{-2 / 3} $$

Solve the given equation. $$ \frac{1}{2}[2 x-3(x-4)]=\frac{2}{3}(x-5) $$

Rewrite the number without using exponents. $$ \frac{2^{-3} \cdot 2^{-4}}{2^{-5} \cdot 2^{-2}} $$

Perform the indicated operations and simplify. $$ \left(5 y^{2}-2 y+1\right)-\left(y^{2}-3 y-7\right) $$

State the real number property that iustifies the statement $$ (2 x+y)+z=z+(2 x+y) $$

Perform the indicated operations and simplify. \(\frac{4 y+12}{y+2} \cdot \frac{3 y+6}{2 y-1}\)

Solve the equation by completing the square. $$ x^{2}-x-6=0 $$

Find the values of \(x\) that satisfy the inequalities. $$ x+1>2 \text { or } x-1<-2 $$

Rewrite the number without radicals or exponents. $$ 81^{-1 / 4} $$

Solve the given equation. $$ \frac{1}{3}[2-3(x+2)]=\frac{1}{4}\left[(-3 x+1)+\frac{1}{2} x\right] $$