Chapter 1

Carry out the indicated operation and write your answer using positive exponents only. $$ \frac{3^{-5 / 4}}{3^{-1 / 4}} $$

Solve the given equation. $$ \frac{1}{x+3}=0 $$

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

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ 4 u^{2}-12 u v+9 v^{2} $$

State the real number property that iustifies the statement $$ (a+2 b)(a-3 b)=a(a-3 b)+2 b(a-3 b) $$

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

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

Find the values of \(x\) that satisfy the inequalities. $$ \frac{x+3}{x-2} \geq 0 $$

Solve the equation by completing the square. $$ 4 x^{2}-13=0 $$

Carry out the indicated operation and write your answer using positive exponents only. $$ \frac{2^{-1 / 2} \cdot 3^{2 / 3}}{2^{3 / 2} \cdot 3^{-1 / 3}} $$

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

Solve the given equation. $$ \frac{2 x-3}{x+1}=\frac{2}{5} $$

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ x^{2}+3 x-4 $$

State the real number property that iustifies the statement $$ a-[-(c+d)]=a+(c+d) $$

Perform the indicated operations and simplify. $$ 2 m(3 m-4)+m(m-1) $$

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

Find the values of \(x\) that satisfy the inequalities. $$ \frac{2 x-3}{x+1} \geq 4 $$

Solve the equation by completing the square. $$ 7 p^{2}-20=0 $$

Carry out the indicated operation and write your answer using positive exponents only. $$ \frac{4^{1 / 3} \cdot 4^{-2 / 5}}{4^{2 / 3}} $$

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

Solve the given equation. $$ \frac{r}{3 r-1}=4 $$

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ 3 m^{3}+3 m^{2}-18 m $$

State the real number property that iustifies the statement $$ -(2 x+y)[-(3 x+2 y)]=(2 x+y)(3 x+2 y) $$

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

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

Find the values of \(x\) that satisfy the inequalities. $$ \frac{x-2}{x-1} \leq 2 $$

Solve the equation by using the quadratic formula. $$ 2 x^{2}-x-6=0 $$

Carry out the indicated operation and write your answer using positive exponents only. $$ \left(2^{3 / 2}\right)^{4} $$

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

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

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ 12 x^{2} y-10 x y-12 y $$

State the real number property that iustifies the statement $$ 0(2 a+3 b)=0 $$

Perform the indicated operations and simplify. $$ 3(2 a-b)-4(b-2 a) $$

Perform the indicated operations and simplify. \(\frac{4}{x^{2}-9}-\frac{5}{x^{2}-6 x+9}\)

Find the values of \(x\) that satisfy the inequalities. $$ \frac{2 x-1}{x+2} \leq 4 $$

Solve the equation by using the quadratic formula. $$ 6 x^{2}-7 x-3=0 $$

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

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

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

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ 12 x^{2} y-2 x y-24 y $$

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

Evaluate the expression. $$ |-6+2| $$

Solve the equation by using the quadratic formula. $$ m^{2}=4 m-1 $$

Perform the indicated operations and simplify. \(\frac{3 y-6}{4 y+6} \div \frac{6 y+24}{8 y+12}\)

Carry out the indicated operation and write your answer using positive exponents only. $$ x^{2 / 5} \cdot x^{-1 / 5} $$

Solve the given equation. $$ \frac{3 k-2}{4}-\frac{3 k}{4}=\frac{k+3}{k} $$

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

State the real number property that iustifies the statement $$ \text { If }(x-2)(2 x+5)=0, \text { then } x=2 \text { or } x=-\frac{5}{2} $$

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

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