Chapter 1

For the following exercises, simplify each expression. \(\sqrt{98}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(11^{3} \div 11^{4}\)

For the following exercises, simplify the rational expressions. \(\frac{3 c^{2}+25 c-18}{3 c^{2}-23 c+14}\)

For the following exercises, factor by grouping. \(6 c^{2}+41 c+63\)

For the following exercises, find the sum or difference. \(\left(4 z^{3}+8 z^{2}-z\right)+\left(-2 z^{2}+z+6\right)\)

For the following exercises, simplify each expression. \(\sqrt{\frac{27}{64}}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(6^{5} \times 6^{-7}\)

For the following exercises, simplify the rational expressions. \(\frac{12 n^{2}-29 n-8}{28 n^{2}-5 n-3}\)

For the following exercises, factor by grouping. \(6 n^{2}-19 n-11\)

For the following exercises, find the sum or difference. \(\left(6 w^{2}+24 w+24\right)-\left(3 w^{2}-6 w+3\right)\)

For the following exercises, simplify each expression. \(\sqrt{\frac{81}{5}}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(\left(8^{0}\right)^{2}\)

For the following exercises, multiply the rational expressions and express the product in simplest form. \(\frac{x^{2}-x-6}{2 x^{2}+x-6} \cdot \frac{2 x^{2}+7 x-15}{x^{2}-9}\)

For the following exercises, factor by grouping. \(20 w^{2}-47 w+24\)

For the following exercises, find the sum or difference. \(\left(7 a^{3}+6 a^{2}-4 a-13\right)+\left(-3 a^{3}-4 a^{2}+6 a+17\right)\)

For the following exercises, simplify each expression. \(\sqrt{800}\)

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

For the following exercises, multiply the rational expressions and express the product in simplest form. \(\frac{c^{2}+2 c-24}{c^{2}+12 c+36} \cdot \frac{c^{2}-10 c+24}{c^{2}-8 c+16}\)

For the following exercises, find the sum or difference. \(\left(11 b^{4}-6 b^{3}+18 b^{2}-4 b+8\right)-\left(3 b^{3}+6 b^{2}+3 b\right)\)

For the following exercises, simplify each expression. \(\sqrt{169}+\sqrt{144}\)

For the following exercises, write each expression with a single base. Do not simplify further. Write answers with positive exponents. \(4^{2} \times 4^{3} \div 4^{-4}\)

For the following exercises, simplify the given expression. \(5+(6+4)-11\)

For the following exercises, multiply the rational expressions and express the product in simplest form. \(\frac{2 d^{2}+9 d-35}{d^{2}+10 d+21} \cdot \frac{3 d^{2}+2 d-21}{3 d^{2}+14 d-49}\)

For the following exercises, factor the polynomial. \(7 x^{2}+48 x-7\)

For the following exercises, find the sum or difference. \(\left(49 p^{2}-25\right)+\left(16 p^{4}-32 p^{2}+16\right)\)

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

For the following exercises, write each expression with a single base. Do not simplify further. Write answers with positive exponents. \(\frac{6^{12}}{6^{9}}\)

For the following exercises, simplify the given expression. \(9-18 \div 3^{2}\)

For the following exercises, multiply the rational expressions and express the product in simplest form. \(\frac{10 h^{2}-9 h-9}{2 h^{2}-19 h+24} \cdot \frac{h^{2}-16 h+64}{5 h^{2}-37 h-24}\)

For the following exercises, factor the polynomial. \(10 h^{2}-9 h-9\)

For the following exercises, find the product. \((4 x+2)(6 x-4)\)

For the following exercises, simplify each expression. \(\frac{18}{\sqrt{162}}\)

For the following exercises, write each expression with a single base. Do not simplify further. Write answers with positive exponents. \(\left(12^{3} \times 12\right)^{10}\)

For the following exercises, simplify the given expression. \(14 \times 3 \div 7-6\)

For the following exercises, multiply the rational expressions and express the product in simplest form. \(\frac{6 b^{2}+13 b+6}{4 b^{2}-9} \cdot \frac{6 b^{2}+31 b-30}{18 b^{2}-3 b-10}\)

For the following exercises, factor the polynomial. \(2 b^{2}-25 b-247\)

For the following exercises, find the product. \(\left(14 c^{2}+4 c\right)\left(2 c^{2}-3 c\right)\)

For the following exercises, simplify each expression. \(\sqrt{192}\)

For the following exercises, write each expression with a single base. Do not simplify further. Write answers with positive exponents. \(10^{6} \div\left(10^{10}\right)^{-2}\)

For the following exercises, simplify the given expression. \(9-(3+11) \times 2\)

For the following exercises, multiply the rational expressions and express the product in simplest form. \(\frac{2 d^{2}+15 d+25}{4 d^{2}-25} \cdot \frac{2 d^{2}-15 d+25}{25 d^{2}-1}\)

For the following exercises, factor the polynomial. \(9 d^{2}-73 d+8\)

For the following exercises, find the product. \(\left(6 b^{2}-6\right)\left(4 b^{2}-4\right)\)

For the following exercises, simplify each expression. \(14 \sqrt{6}-6 \sqrt{24}\)

For the following exercises, write each expression with a single base. Do not simplify further. Write answers with positive exponents. \(7^{-6} \times 7^{-3}\)

For the following exercises, simplify the given expression. \(6+2 \times 2-1\)

For the following exercises, multiply the rational expressions and express the product in simplest form. \(\frac{6 x^{2}-5 x-50}{15 x^{2}-44 x-20} \cdot \frac{20 x^{2}-7 x-6}{2 x^{2}+9 x+10}\)

For the following exercises, factor the polynomial. \(90 v^{2}-181 v+90\)

For the following exercises, find the product. \((3 d-5)(2 d+9)\)

For the following exercises, simplify each expression. \(15 \sqrt{5}+7 \sqrt{45}\)