Chapter 1

Evaluate the expression. $$ 4+|-4| $$

Solve the equation by using the quadratic formula. $$ 2 x^{2}=8 x-3 $$

Carry out the indicated operation and write your answer using positive exponents only. $$ y^{-3 / 8} \cdot y^{1 / 4} $$

Simplify the expression, writing your answer using positive exponents only. $$ \left(\frac{1}{2} u^{-2} v^{3}\right)\left(4 v^{3}\right) $$

Solve the given equation. $$ \frac{2 x-1}{3 x+2}=\frac{2 x+1}{3 x+1} $$

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ 6 u v^{2}+9 u v-6 v $$

State the real number property that iustifies the statement $$ \text { If } x(2 x-9)=0, \text { then } x=0 \text { or } x=\frac{9}{2} \text { . } $$

Perform the indicated operations and simplify. $$ (3 r-1)(2 r+5) $$

Perform the indicated operations and simplify. \(\frac{x}{1-x}+\frac{2 x+3}{x^{2}-1}\)

Evaluate the expression. $$ \frac{|-12+4|}{|16-12|} $$

Solve the equation by using the quadratic formula. $$ 8 x+3=8 x^{2} $$

Carry out the indicated operation and write your answer using positive exponents only. $$ \frac{x^{3 / 4}}{x^{-1 / 4}} $$

Simplify the expression, writing your answer using positive exponents only. $$ \left(-x^{2} y\right)^{3}\left(\frac{2 y^{2}}{x^{4}}\right) $$

Solve the given equation. $$ \frac{m-2}{m}+\frac{2}{m}=\frac{m+3}{m-3} $$

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

State the real number property that iustifies the statement $$ \frac{(x+1)(x-3)}{(2 x+1)(x-3)}=\frac{x+1}{2 x+1} $$

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

Perform the indicated operations and simplify. \(2+\frac{1}{a+2}-\frac{2 a}{a-2}\)

Evaluate the expression. $$ \left|\frac{0.2-1.4}{1.6-2.4}\right| $$

Solve the equation by using the quadratic formula. $$ 6 p-6=p^{2} $$

Carry out the indicated operation and write your answer using positive exponents only. $$ \frac{x^{7 / 3}}{x^{-2}} $$

Solve the given equation. $$ \frac{4}{x(x-2)}=\frac{2}{x-2} $$

Simplify the expression, writing your answer using positive exponents only. $$ \left(-\frac{1}{2} x^{2} y\right)^{-2} $$

State the real number property that iustifies the statement $$ \frac{(2 x+1)(x+3)}{(2 x-1)(x+3)}=\frac{2 x+1}{2 x-1} $$

Perform the indicated operations and simplify. $$ (5 m-2 n)(5 m+3 n) $$

Perform the indicated operations and simplify. \(x-\frac{x^{2}}{x+2}+\frac{2}{x-2}\)

Evaluate the expression. $$ \sqrt{3}|-2|+3|-\sqrt{3}| $$

Solve the equation by using the quadratic formula. $$ 4 x=-2 x^{2}+3 $$

Carry out the indicated operation and write your answer using positive exponents only. $$ \left(\frac{x^{3}}{-27 x^{-6}}\right)^{-2 / 3} $$

Simplify the expression, writing your answer using positive exponents only. $$ \left(\frac{2 u^{2} v^{3}}{3 u v}\right)^{-1} $$

Solve the given equation. $$ \sqrt{3 x+1}=2 $$

State the real number property that iustifies the statement $$ \frac{a+b}{b} \div \frac{a-b}{a b}=\frac{a(a+b)}{a-b} $$

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

Perform the indicated operations and simplify. \(\frac{y}{y^{2}-1}+\frac{y-1}{y+1}-\frac{2 y}{1-y}\)

Evaluate the expression. $$ |-1|+\sqrt{2}|-2| $$

Solve the equation by using the quadratic formula. $$ 15-2 y^{2}=7 y $$

Carry out the indicated operation and write your answer using positive exponents only. $$ \left(\frac{27 x^{-3} y^{2}}{8 x^{-2} y^{-5}}\right)^{1 / 3} $$

Simplify the expression, writing your answer using positive exponents only. $$ \left(\frac{a^{-2}}{2 b^{2}}\right)^{-3} $$

Solve the given equation. $$ \sqrt{2 x-3}-3=0 $$

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ 16 u^{4} v-9 v^{3} $$

State the real number property that iustifies the statement $$ \frac{x+2 y}{3 x+y} \div \frac{x}{6 x+2 y}=\frac{x+2 y}{3 x+y} \cdot \frac{2(3 x+y)}{x}=\frac{2(x+2 y)}{x} $$

Perform the indicated operations and simplify. $$ (2 m+3 n)(3 m-2 n) $$

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

Evaluate the expression. $$ |\pi-1|+2 $$

Solve the equation by using the quadratic formula. $$ 2.1 x^{2}-4.7 x-6.2=0 $$

Carry out the indicated operation and write your answer using positive exponents only. $$ \left(\frac{x^{-3}}{y^{-2}}\right)^{1 / 2}\left(\frac{y}{x}\right)^{3 / 2} $$

Solve the given equation. $$ \sqrt{k^{2}-4}=4-k $$

Simplify the expression, writing your answer using positive exponents only. $$ \left(3 x^{-2}\right)^{3}\left(2 x^{2}\right)^{5} $$

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ (a-2 b)^{2}-(a+2 b)^{2} $$

State the real number property that iustifies the statement $$ \frac{a}{b+c}+\frac{c}{b}=\frac{a b+b c+c^{2}}{b(b+c)} $$