Chapter 1

Express the number in the form \(a / b,\) where \(a\) and \(b\) are integers. $$\left(-\frac{2}{3}\right)^{4}$$

Solve the equation. \(4 x-3=-5 x+6\)

Rewrite the expression without using the absolute value symbol, and simplify the result. $$|x+3| \text { if } x \leq-3$$

If \(x<0\) and \(y>0,\) determine the sign of the real number. (a) \(x y\) (b) \(x^{2} y\) (c) \(\frac{x}{y}+x\) (d) \(y-x\)

Express as a polynomial. $$(2 u+3)(u-4)+4 u(u-2)$$

Write the expression in the form \(a+b i,\) where \(a\) and \(b\) are real numbers. $$(5-2 i)+(-3+6 i)$$

Express the number in the form \(a / b,\) where \(a\) and \(b\) are integers. $$(-3)^{3}$$

Solve the equation. \(5 x-4=2(x-2)\)

Rewrite the expression without using the absolute value symbol, and simplify the result. $$|(x-2)(x-3)| \text { if } 2

If \(x<0\) and \(y>0,\) determine the sign of the real number. (a) \(\frac{x}{y}\) (b) \(x y^{2}\) (c) \(\frac{x-y}{x y}\) (d) \(y(y-x)\)

Express as a polynomial. $$(3 u-1)(u+2)+7 u(u+1)$$

Write the expression in the form \(a+b i,\) where \(a\) and \(b\) are real numbers. $$(-5+7 i)+(4+9 i)$$

Express the number in the form \(a / b,\) where \(a\) and \(b\) are integers. $$\frac{2^{-3}}{3^{-2}}$$

Replace the symbol \square with elther \(<,>,\) or \(=\) to make the resulting statement true. (a) \(-7 \square-4\) (b) \(\frac{\pi}{2} \square 1.57\) (c) \(\sqrt{225} \square 15\)

Solve the equation. \((3 x-2)^{2}=(x-5)(9 x+4)\)

Simplify the expression, and rationalize the denominator when appropriate. $$\left(\frac{a^{2 / 3} b^{3 / 2}}{a^{2} b}\right)$$

Express as a polynomial. $$\frac{8 x^{2} y^{3}-10 x^{3} y}{2 x^{2} y}$$

Write the expression in the form \(a+b i,\) where \(a\) and \(b\) are real numbers. $$(7-6 i)-(-11-3 i)$$

Express the number in the form \(a / b,\) where \(a\) and \(b\) are integers. $$\frac{2^{0}+0^{2}}{2+0}$$

Replace the symbol \square with elther \(<,>,\) or \(=\) to make the resulting statement true. (a) \(-3 \square-5\) (b) \(\frac{\pi}{4} \square 0.8\) (c) \(\sqrt{289} \square 17\)

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

Simplify the expression, and rationalize the denominator when appropriate. $$\left(-2 p^{2} q\right)^{3}\left(\frac{p}{4 q^{2}}\right)^{2}$$

Express as a polynomial. $$\frac{6 x^{2} y z^{3}-x y^{2} z}{x y z}$$

Write the expression in the form \(a+b i,\) where \(a\) and \(b\) are real numbers. $$(-3+8 i)-(2+3 i)$$

Express the number in the form \(a / b,\) where \(a\) and \(b\) are integers. $$-2^{4}+3^{-1}$$

Replace the symbol \square with elther \(<,>,\) or \(=\) to make the resulting statement true. (a) \(\frac{1}{11} \square 0.09\) (b) \(\frac{2}{3} \square 0.6666\) (c) \(\frac{22}{7} \square \pi\)

Solve the equation. \(\frac{3 x+1}{6 x-2}=\frac{2 x+5}{4 x-13}\)

Simplify the expression, and rationalize the denominator when appropriate. $$\left(\frac{x y^{-1}}{\sqrt{z}}\right)^{4} \div\left(\frac{x^{1 / 3} y^{2}}{z}\right)^{3}$$

Express as a polynomial. $$(2 x+3 y)(2 x-3 y)$$

Write the expression in the form \(a+b i,\) where \(a\) and \(b\) are real numbers. $$(3+5 i)(2-7 i)$$

Express the number in the form \(a / b,\) where \(a\) and \(b\) are integers. $$\left(-\frac{3}{2}\right)^{4}-2^{-4}$$

Replace the symbol \square with elther \(<,>,\) or \(=\) to make the resulting statement true. (a) \(\frac{1}{7} \square 0.143\) (b) \(\frac{5}{6} \square 0.833\) (c) \(\sqrt{2} \square 1.4\)

Solve the equation. \(\frac{5 x+2}{10 x-3}=\frac{x-8}{2 x+3}\)

Simplify the expression, and rationalize the denominator when appropriate. $$\left(\frac{-64 x^{3}}{z^{6} y^{9}}\right)^{2 / 3}$$

Express as a polynomial. $$(5 x+4 y)(5 x-4 y)$$

Write the expression in the form \(a+b i,\) where \(a\) and \(b\) are real numbers. $$(-2+6 i)(8-i)$$

Express the number in the form \(a / b,\) where \(a\) and \(b\) are integers. $$16^{-3 / 4}$$

Express the statement as an inequality. (a) \(x\) is negative. (b) \(y\) is nonnegative. (c) \(q\) is less than or equal to \(\pi\). (d) \(d\) is between 4 and 2 . (e) \(t\) is not less than 5 . (f) The negative of \(z\) is not greater than 3 . (g) The quotient of \(p\) and \(q\) is at most 7. (h) The reciprocal of \(w\) is at least 9 . (i) The absolute value of \(x\) is greater than 7 .

Solve the equation. \(\frac{4}{x+2}+\frac{1}{x-2}=\frac{5 x-6}{x^{2}-4}\)

Simplify the expression, and rationalize the denominator when appropriate. $$\left[\left(a^{23} b^{-2}\right)^{3}\right]^{-1}$$

Express as a polynomial. $$(3 x+2 y)^{2}$$

Write the expression in the form \(a+b i,\) where \(a\) and \(b\) are real numbers. $$(1-3 i)(2+5 i)$$

Express the number in the form \(a / b,\) where \(a\) and \(b\) are integers. $$9^{1 / 2}$$

Express the statement as an inequality. (a) \(b\) is positive. (b) \(s\) is nonpositive. (c) \(w\) is greater than or equal to \(-4\). (d) \(c\) is between \(\frac{1}{5}\) and \(\frac{1}{3}\). (e) \(p\) is not greater than \(-2\). (f) The negative of \(m\) is not less than \(-2\). (g) The quotient of \(r\) and \(s\) is at least \(\frac{1}{s}\). (h) The reciprocal of \(f\) is at most 14. (i) The absolute value of \(x\) is less than 4.

Solve the equation. \(\frac{2}{2 x+5}+\frac{3}{2 x-5}=\frac{10 x+5}{4 x^{2}-25}\)

Simplify the expression, and rationalize the denominator when appropriate. $$x^{-2}-y^{-1}$$

Express as a polynomial. $$(5 x-4 y)^{2}$$

Write the expression in the form \(a+b i,\) where \(a\) and \(b\) are real numbers. $$(8+2 i)(7-3 i)$$

Rewrite the number without using the absolute value symbol, and simplify the result. (a) \(|-3-2|\) (b) \(|-5|-|2| \) (c) \(|7|+|-4|\)

Express the number in the form \(a / b,\) where \(a\) and \(b\) are integers. $$(-0.008)^{2 / 3}$$