Chapter 1

For the following exercises, simplify each expression. \(\frac{8}{1-\sqrt{17}}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(a b^{2} \div d^{-3}\)

For the following exercises, solve for the variable. \(4 y+8-2 y\) for \(y=3\)

For the following exercises, divide the rational expressions. \(\frac{16 a^{2}-24 a+9}{4 a^{2}+17 a-15} \div \frac{16 a^{2}-9}{4 a^{2}+11 a+6}\)

For the following exercises, factor the polynomial. \(16 a^{2}-8 a+1\)

For the following exercises, expand the binomial \((9 b+1)^{2}\)

For the following exercises, simplify each expression. \(\sqrt[4]{16}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(\left(w^{0} x^{5}\right)^{-1}\)

For the following exercises, solve for the variable. \((11 a+3)-18 a+4\) for \(a=-2\)

For the following exercises, divide the rational expressions. \(\frac{22 y^{2}+59 y+10}{12 y^{2}+28 y-5} \div \frac{11 y^{2}+46 y+8}{24 y^{2}-10 y+1}\)

For the following exercises, factor the polynomial. \(49 n^{2}+168 n+144\)

For the following exercises, multiply the binomials. \((4 c+1)(4 c-1)\)

For the following exercises, simplify each expression. \(\sqrt[3]{128}+3 \sqrt[3]{2}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(\frac{m^{4}}{n^{0}}\)

For the following exercises, solve for the variable. \(4 z-2 z(1+4)-36\) for \(z=5\)

For the following exercises, divide the rational expressions. \(\frac{9 x^{2}+3 x-20}{3 x^{2}-7 x+4} \div \frac{6 x^{2}+4 x-10}{x^{2}-2 x+1}\)

For the following exercises, factor the polynomial. \(121 x^{2}-88 x+16\)

For the following exercises, multiply the binomials. \((9 a-4)(9 a+4)\)

For the following exercises, simplify each expression. \(\sqrt[5]{\frac{-32}{243}}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(y^{-4}\left(y^{2}\right)^{2}\)

For the following exercises, solve for the variable. \(4 y(7-2)^{2}+200\) for \(y=-2\)

For the following exercises, factor the polynomial. \(225 y^{2}+120 y+16\)

For the following exercises, multiply the binomials. \((15 n-6)(15 n+6)\)

For the following exercises, simplify each expression. \(\frac{15 \sqrt[4]{125}}{\sqrt[4]{5}}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(\frac{p^{-4} q^{2}}{p^{2} q^{-3}}\)

For the following exercises, solve for the variable. \(-(2 x)^{2}+1+3\) for \(x=2\)

For the following exercises, add and subtract the rational expressions, and then simplify. \(\frac{12}{2 q}-\frac{6}{3 p}\)

For the following exercises, factor the polynomial. \(m^{2}-20 m+100\)

For the following exercises, multiply the binomials. \((25 b+2)(25 b-2)\)

For the following exercises, simplify each expression. \(3 \sqrt[3]{-432}+\sqrt[3]{16}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \((l \times w)^{2}\)

For the following exercises, add and subtract the rational expressions, and then simplify. \(\frac{4}{a+1}+\frac{5}{a-3}\)

For the following exercises, factor the polynomial. \(25 p^{2}-120 m+144\)

For the following exercises, multiply the binomials. \((4+4 m)(4-4 m)\)

For the following exercises, simplify each expression. \(\sqrt{400 x^{4}}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(\left(y^{7}\right)^{3} \div x^{14}\)

For the following exercises, solve for the variable. \(2(11 c-4)-36\) for \(c=0\)

For the following exercises, add and subtract the rational expressions, and then simplify. \(\frac{c+2}{3}-\frac{c-4}{4}\)

For the following exercises, factor the polynomial. \(36 q^{2}+60 q+25\)

For the following exercises, multiply the binomials. \((14 p+7)(14 p-7)\)

For the following exercises, simplify each expression. \(\sqrt{4 y^{2}}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(\left(\frac{a}{2^{3}}\right)^{2}\)

For the following exercises, add and subtract the rational expressions, and then simplify. \(\frac{y+3}{y-2}+\frac{y-3}{y+1}\)

For the following exercises, factor the polynomials. \(x^{3}+216\)

For the following exercises, multiply the binomials. \((11 q-10)(11 q+10)\)

For the following exercises, simplify each expression. \(\sqrt{49 p}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(5^{2} m \div 5^{0} m\)

For the following exercises, solve for the variable. \(\frac{1}{4}\left(8 w-4^{2}\right)\) for \(w=1\)

For the following exercises, add and subtract the rational expressions, and then simplify. \(\frac{x-1}{x+1}-\frac{2 x+3}{2 x+1}\)

For the following exercises, factor the polynomials. \(27 y^{3}-8\)