Chapter 1

For the following exercises, write each expression with a single base. Do not simplify further. Write answers with positive exponents. \(\left(3^{3} \div 3^{4}\right)^{5}\)

For the following exercises, simplify the given expression. \(64 \div(8+4 \times 2)\)

For the following exercises, multiply the rational expressions and express the product in simplest form. \(\frac{t^{2}-1}{t^{2}+4 t+3} \cdot \frac{t^{2}+2 t-15}{t^{2}-4 t+3}\)

For the following exercises, factor the polynomial. \(12 t^{2}+t-13\)

For the following exercises, find the product. \((9 v-11)(11 v-9)\)

For the following exercises, simplify each expression. \(\sqrt{150}\)

For the following exercises, express the decimal in scientific notation. 0.0000314

For the following exercises, simplify the given expression. \(9+4\left(2^{2}\right)\)

For the following exercises, multiply the rational expressions and express the product in simplest form. \(\frac{2 n^{2}-n-15}{6 n^{2}+13 n-5} \cdot \frac{12 n^{2}-13 n+3}{4 n^{2}-15 n+9}\)

For the following exercises, factor the polynomial. \(2 n^{2}-n-15\)

For the following exercises, find the product. \(\left(4 t^{2}+7 t\right)\left(-3 t^{2}+4\right)\)

For the following exercises, simplify each expression. \(\sqrt{\frac{96}{100}}\)

For the following exercises, express the decimal in scientific notation. 148,000,000

For the following exercises, simplify the given expression. \((12 \div 3 \times 3)^{2}\)

For the following exercises, multiply the rational expressions and express the product in simplest form. \(\frac{36 x^{2}-25}{6 x^{2}+65 x+50} \cdot \frac{3 x^{2}+32 x+20}{18 x^{2}+27 x+10}\)

For the following exercises, factor the polynomial. \(16 x^{2}-100\)

For the following exercises, find the product. \((8 n-4)\left(n^{2}+9\right)\)

For the following exercises, simplify each expression. \((\sqrt{42})(\sqrt{30})\)

For the following exercises, convert each number in scientific notation to standard notation. \(1.6 \times 10^{10}\)

For the following exercises, simplify the given expression. \(25 \div 5^{2}-7\)

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

For the following exercises, factor the polynomial. \(25 y^{2}-196\)

For the following exercises, expand the binomial \((4 x+5)^{2}\)

For the following exercises, simplify each expression. \(12 \sqrt{3}-4 \sqrt{75}\)

For the following exercises, convert each number in scientific notation to standard notation. \(9.8 \times 10^{-9}\)

For the following exercises, simplify the given expression. \((15-7) \times(3-7)\)

For the following exercises, divide the rational expressions. \(\frac{6 p^{2}+p-12}{8 p^{2}+18 p+9} \div \frac{6 p^{2}-11 p+4}{2 p^{2}+11 p-6}\)

For the following exercises, factor the polynomial. \(121 p^{2}-169\)

For the following exercises, expand the binomial \((3 y-7)^{2}\)

For the following exercises, simplify each expression. \(\sqrt{\frac{4}{225}}\)

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

For the following exercises, divide the rational expressions. \(\frac{q^{2}-9}{q^{2}+6 q+9} \div \frac{q^{2}-2 q-3}{q^{2}+2 q-3}\)

For the following exercises, factor the polynomial. \(4 m^{2}-9\)

For the following exercises, expand the binomial \((12-4 x)^{2}\)

For the following exercises, simplify each expression. \(\sqrt{\frac{405}{324}}\)

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

For the following exercises, divide the rational expressions. \(\frac{18 d^{2}+77 d-18}{27 d^{2}-15 d+2} \div \frac{3 d^{2}+29 d-44}{9 d^{2}-15 d+4}\)

For the following exercises, factor the polynomial. \(361 d^{2}-81\)

For the following exercises, expand the binomial \((4 p+9)^{2}\)

For the following exercises, simplify each expression. \(\sqrt{\frac{360}{361}}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(\left(b^{3} c^{4}\right)^{2}\)

For the following exercises, divide the rational expressions. \(\frac{16 x^{2}+18 x-55}{32 x^{2}-36 x-11} \div \frac{2 x^{2}+17 x+30}{4 x^{2}+25 x+6}\)

For the following exercises, factor the polynomial. \(324 x^{2}-121\)

For the following exercises, expand the binomial \((2 m-3)^{2}\)

For the following exercises, simplify each expression. \(\frac{5}{1+\sqrt{3}}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(\left(\frac{x^{-3}}{y^{2}}\right)^{-5}\)

For the following exercises, solve for the variable. \(8(x+3)-64\) for \(x=2\)

For the following exercises, divide the rational expressions. \(\frac{144 b^{2}-25}{72 b^{2}-6 b-10} \div \frac{18 b^{2}-21 b+5}{36 b^{2}-18 b-10}\)

For the following exercises, factor the polynomial. \(144 b^{2}-25 c^{2}\)

For the following exercises, expand the binomial \((3 y-6)^{2}\)