Chapter 1

For the following exercises, multiply the polynomials. \(\left(2 x^{2}+2 x+1\right)(4 x-1)\)

For the following exercises, simplify each expression. \(\left(144 p^{2} q^{6}\right)^{\frac{1}{2}}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(\frac{(16 \sqrt{x})^{2}}{y^{-1}}\)

For the following exercises, simplify the expression. \(4 x+x(13-7)\)

For the following exercises, add and subtract the rational expressions, and then simplify. \(\frac{3 z}{z+1}+\frac{2 z+5}{z-2}\)

For the following exercises, factor the polynomials. \(125 a^{3}+343\)

For the following exercises, multiply the polynomials. \(\left(4 t^{2}+t-7\right)\left(4 t^{2}-1\right)\)

For the following exercises, simplify each expression. \(m^{\frac{5}{2}} \sqrt{289}\)

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

For the following exercises, simplify the expression. \(2 y-(4)^{2} y-11\)

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

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

For the following exercises, multiply the polynomials. \((x-1)\left(x^{2}-2 x+1\right)\)

For the following exercises, simplify each expression. \(9 \sqrt{3 m^{2}}+\sqrt{27}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(\left(m a^{6}\right)^{2} \frac{1}{m^{3} a^{2}}\)

For the following exercises, simplify the expression. \(\frac{a}{2^{3}}(64)-12 a \div 6\)

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

For the following exercises, factor the polynomials. \(64 x^{3}-125\)

For the following exercises, multiply the polynomials. \((y-2)\left(y^{2}-4 y-9\right)\)

For the following exercises, simplify each expression. \(3 \sqrt{a b^{2}}-b \sqrt{a}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(\left(b^{-3} c\right)^{3}\)

For the following exercises, simplify the expression. \(8 b-4 b(3)+1\)

For the following exercises, simplify the rational expression. \(\frac{\frac{6}{y}-\frac{4}{x}}{y}\)

For the following exercises, factor the polynomials. \(729 q^{3}+1331\)

For the following exercises, multiply the polynomials. \((6 k-5)\left(6 k^{2}+5 k-1\right)\)

For the following exercises, simplify each expression. \(\frac{4 \sqrt{2 n}}{\sqrt{16 n^{4}}}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(\left(x^{2} y^{13} \div y^{0}\right)^{2}\)

For the following exercises, simplify the expression. \(5 l \div 3 l \times(9-6)\)

For the following exercises, simplify the rational expression. \(\frac{\frac{2}{a}+\frac{7}{b}}{b}\)

For the following exercises, factor the polynomials. \(125 r^{3}+1,728 s^{3}\)

For the following exercises, multiply the polynomials. \(\left(3 p^{2}+2 p-10\right)(p-1)\)

For the following exercises, simplify each expression. \(\sqrt{\frac{225 x^{3}}{49 x}}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(\left(9 z^{3}\right)^{-2} y\)

For the following exercises, simplify the expression. \(7 z-3+z \times 6^{2}\)

For the following exercises, simplify the rational expression. \(\frac{\frac{x}{4}-\frac{p}{8}}{p}\)

For the following exercises, factor the polynomials. \(4 x(x-1)^{-\frac{2}{3}}+3(x-1)^{\frac{1}{3}}\)

For the following exercises, multiply the polynomials. \((4 m-13)\left(2 m^{2}-7 m+9\right)\)

For the following exercises, simplify each expression. \(3 \sqrt{44 z}+\sqrt{99 z}\)

To reach escape velocity, a rocket must travel at the rate of \(2.2 \times 10^{6} \mathrm{ft} / \mathrm{min}\). Rewrite the rate in standard notation.

For the following exercises, simplify the expression. \(4 \times 3+18 x \div 9-12\)

For the following exercises, simplify the rational expression. \(\frac{\frac{3}{a}+\frac{b}{6}}{\frac{2 b}{3 a}}\)

For the following exercises, factor the polynomials. \(3 c(2 c+3)^{-\frac{1}{4}}-5(2 c+3)^{\frac{3}{4}}\)

For the following exercises, multiply the polynomials. \((a+b)(a-b)\)

For the following exercises, simplify each expression. \(\sqrt{50 y^{8}}\)

A dime is the thinnest coin in U.S. currency. A dime's thickness measures \(1.35 \times 10^{-3}\) \(\mathrm{m}\). Rewrite the number in standard notation.

For the following exercises, simplify the expression. \(9(y+8)-27\)

For the following exercises, simplify the rational expression. \(\frac{\frac{3}{x+1}+\frac{2}{x-1}}{\frac{x-1}{x+1}}\)

For the following exercises, factor the polynomials. \(3 t(10 t+3)^{\frac{1}{3}}+7(10 t+3)^{\frac{4}{3}}\)

For the following exercises, multiply the polynomials. \((4 x-6 y)(6 x-4 y)\)

For the following exercises, simplify each expression. \(\sqrt{490 b c^{2}}\)