Chapter 1

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

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ 12 x^{2}-3 y^{2} $$

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

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

Perform the indicated operations and simplify. \(\frac{2 m+6}{3} \div \frac{3 m+9}{6}\)

Solve the equation by completing the square. $$ 6 x^{2}-12 x=3 $$

Find the values of \(x\) that satisfy the inequalities. $$ x+3>1 \text { and } x-2<1 $$

Rewrite the number without radicals or exponents. $$ -\left(\frac{27}{8}\right)^{-1 / 3} $$

Solve the given equation. $$ (2 x+1)^{2}-(3 x-2)^{2}=5 x(2-x) $$

Rewrite the number without using exponents. $$ \left(\frac{3^{4} \cdot 3^{-3}}{3^{-2}}\right)^{-1} $$

Perform the indicated operations and simplify. $$ \left(2.4 x^{3}-3 x^{2}+1.7 x-6.2\right)-\left(1.2 x^{3}+1.2 x^{2}-0.8 x+2\right) $$

State the real number property that iustifies the statement $$ u(3 v+w)=(3 v+w) u $$

Find the values of \(x\) that satisfy the inequalities. $$ x-4 \leq 1 \text { and } x+3>2 $$

Solve the equation by completing the square. $$ 2 x^{2}-6 x=20 $$

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

Solve the given equation. $$ x\left[(2 x-3)^{2}+5 x^{2}\right]=3 x^{2}(3 x-4)+18 $$

Rewrite the number without using exponents. $$ \left(\frac{5^{-2} \cdot 5^{-2}}{5^{-5}}\right)^{-2} $$

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ 4 a^{2} b^{2}-25 c^{2} $$

Perform the indicated operations and simplify. $$ \left(1.4 x^{3}-1.2 x^{2}+3.2\right)-\left(-0.8 x^{3}-2.1 x-1.8\right) $$

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

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

Find the values of \(x\) that satisfy the inequalities. $$ (x+3)(x-5) \leq 0 $$

Solve the equation by completing the square. $$ m^{2}-3=-m $$

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

Solve the given equation. $$ \frac{8}{x}=16 $$

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

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

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

State the real number property that iustifies the statement $$ u(2 v+w)=2 u v+u w $$

Perform the indicated operations and simplify. \(\frac{x^{2}-x-6}{2 x^{2}+7 x+6} \cdot \frac{2 x^{2}-x-6}{x^{2}+x-6}\)

Find the values of \(x\) that satisfy the inequalities. $$ (2 x-4)(x+2) \geq 0 $$

Solve the equation by completing the square. $$ p^{2}-4=-2 p $$

Carry out the indicated operation and write your answer using positive exponents only. $$ 2^{6 / 5} \cdot 2^{-1 / 5} $$

Solve the given equation. $$ \frac{1}{x}+\frac{2}{x}=6 $$

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

In Exercises, factor the polynomial. If the polynomial is prime, state it. $$ u^{2}+25 v^{2} $$

State the real number property that iustifies the statement $$ (2 u+v) w=2 u w+v w $$

Perform the indicated operations and simplify. $$ \left(-2 r s^{2}\right)\left(4 r^{2} s^{2}\right)(2 s) $$

Perform the indicated operations and simplify. \(\frac{k^{2}-2 k-3}{k^{2}-k-6} \div \frac{k^{2}-6 k+8}{k^{2}-2 k-8}\)

Find the values of \(x\) that satisfy the inequalities. $$ (2 x-3)(x-1) \geq 0 $$

Solve the equation by completing the square. $$ 3 x-4=-2 x^{2} $$

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

Solve the given equation. $$ \frac{2}{y-1}=4 $$

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

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

State the real number property that iustifies the statement $$ (2 x+3 y)+(x+4 y)=2 x+[3 y+(x+4 y)] $$

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

Perform the indicated operations and simplify. \(\frac{6 y^{2}-5 y-6}{6 y^{2}+13 y+6} \div \frac{6 y^{2}-13 y+6}{9 y^{2}-12 y+4}\)

Find the values of \(x\) that satisfy the inequalities. $$ (3 x-4)(2 x+2) \leq 0 $$

Solve the equation by completing the square. $$ 10 x-5=4 x^{2} $$