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Chapter 18: Theory of Exponents - Exercises

Simplify and express with positive exponents:

  1. \(a^3 \times a^{-5}\)
  2. \((x^{-2})^{-3}\)
  3. \(\frac{x^{\frac{1}{2}}}{x^{\frac{1}{3}}}\)
  4. \((8a^3)^{-\frac{1}{3}}\)
  5. Evaluate: \(5^0 + 4^{-1} - \left(\frac{1}{2}\right)^{-2}\)

Answer Key

  1. \(\frac{1}{a^2}\)
  2. \(x^6\)
  3. \(x^{\frac{1}{6}}\) or \(\sqrt[6]{x}\)
  4. \(\frac{1}{2a}\)
  5. \(1 + \frac{1}{4} - 4 = -\frac{11}{4}\) or \(-2\frac{3}{4}\)