Section 1.2: Exponents and Radicals

  1. Evaluate each expression without using a calculator.  solution

    2. (a) \((-3)^{4}\)   (b) \(-3^{4}\)   (c) \(3^{-4}\)   (d) \(\frac{5^{23}}{5^{21}}\) (e) \(\left(\frac{2}{3}\right)^{-2}\)  (f) \(16^{-3 / 4}\)

  2. Simplify each expression. Write your answer without negative exponents.  solution

    3. (a) \(\sqrt{200}-\sqrt{32}\)   (b) \(\left(3 a^{3} b^{3}\right)\left(4 a b^{2}\right)^{2}\)   (c) \(\left(\dfrac{3 x^{3 / 2} y^{3}}{x^{2} y^{-1 / 2}}\right)^{-2}\)

  3. Evaluate each expression. (Simplify your answers completely.)   solution

    4. (a) \(5\sqrt[3]{81} \)   (b) \( \dfrac{\sqrt{50}}{20} \)   (c) \( \sqrt{\dfrac{25}{12}} \)

  4. Write each expression using rational exponents and simplify. Eliminate any negative exponents. Assume that all letters denote positive numbers.   solution

    5. (a) \(\sqrt[7]{x^5 y^2} \: \sqrt[14]{x^4 y^{38}}\)   (b) \(\dfrac{\sqrt[3]{8 x^5}}{\sqrt{x}}\)