Power law exercises (repetition)

Exercise 1

Convert to a single power (if possible) of the form a⋅bxa\cdot b^x:

  1. x2⋅x5x^2\cdot x^5
  2. x2⋅x5⋅x0.5x^2\cdot x^5 \cdot x^{0.5}
  3. x34\sqrt[4]{x^3}
  4. x\sqrt{x}
  5. 1x2\frac{1}{x^2}
  6. 2x\frac{2}{x}
  7. 3x4\frac{3}{x^4}
  8. 5x3\frac{5}{\sqrt[3]{x}}
  9. 22
  10. 2x2⋅4x⋅5x2x^2\cdot 4x\cdot5\sqrt{x}
  11. xx⋅1xx\sqrt{x}\cdot\frac{1}{x}
  12. 2x−2\frac{2}{x^{-2}}
  13. x3⋅x2x^3\cdot \sqrt{x^2}
  14. x⋅1x2\sqrt{x}\cdot \frac{1}{x^2}
  15. x2⋅x3⋅x5x^2\cdot x^3\cdot \sqrt{x^5}
  16. 3x2⋅6x43x^2\cdot 6x^4
  17. x2+4\sqrt{x^2+4}
  18. 1x⋅x\frac{1}{x\cdot x}
  19. 3x⋅x2\frac{3}{x}\cdot x^2
  20. (x2)3(x^2)^3
  21. (3x3)4(3x^3)^4
  22. (2x3)5\left(2\sqrt{x^3} \right)^5
  23. 8x2x\frac{8x^2}{x}