Honors Algebra 2: Extra Problems on Exponents and Radicals



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  1. Simplify: \( \displaystyle \left( x^{-1} - y^{-1} \right)^{-1} \)
  2. Solution

    \( \displaystyle \frac{xy}{y-x} \)

  3. Simplify: \( \displaystyle \frac{x^{-1} + y^{-1}}{x^{-2}-y^{-2}} \)
  4. Solution

    \( \displaystyle \frac{xy}{y-x} \)

  5. Simplify: \( \displaystyle \sqrt[3]{x^2} \cdot \sqrt[5]{x^3} \cdot \sqrt[6]{x} \)
  6. Solution

    \( \displaystyle x\sqrt[30]{x^{13}} \)

  7. Simplify: \( \displaystyle \sqrt{a \cdot \sqrt[3]{a}} \)
  8. Solution

    \( \displaystyle \sqrt[3]{a^2} \)

  9. Simplify: \( \displaystyle \left( \frac{27^{\frac{4}{3}} - 27^0}{ \left( 3^2 + 4^2 \right)^{\frac{1}{2}}} \right)^ \frac{3}{4} \)
  10. Solution

    \( \displaystyle 8 \)

  11. Simplify: \( \displaystyle \left( \frac{a^{-2}b^{\frac{2}{3}}}{b^{-\frac{1}{2}}} \right)^{-4} \)
  12. Solution

    \( \displaystyle \frac{a^8}{b^{\frac{14}{3}}} \)

  13. Simplify: \( \displaystyle \frac{3^{-1}}{3^{-2}+3^{-3}} \)
  14. Solution

    \( \displaystyle \frac{9}{4} \)

  15. Solve: \( \displaystyle 4^{x+1} = \left( \frac{1}{2} \right)^{-3x} \)
  16. Solution

    \( \displaystyle 2 \)

  17. Solve: \( \displaystyle 2^{4x}\cdot 4^{x - 3} = 64^{x - 1} \)
  18. Solution

    \( \displaystyle x \in \mathbb{R} \)

  19. Solve: \( \displaystyle 3 \left( x - 4 \right)^{\frac{1}{2}} = 15 \)
  20. Solution

    \( \displaystyle 29 \)

  21. Solve: \( \displaystyle x^{\frac{2}{3}} - 3x^{\frac{1}{3}} = -2 \)
  22. Solution

    \( \displaystyle x = \{ 1, 8 \} \)