Worksheet Test

Answer the following questions:

1. What is the value of 2^(1/2)?
2. What is the value of 4^(1/3)?
3. What is the value of 8^(2/3)?
4. What is the value of 16^(1/4)?
5. What is the value of 10^(1/2) * 10^(1/4)?
6. What is the value of (27^(1/3))^2?
7. What is the value of (2^(1/2))^3?
8. What is the value of (3^(1/3))^(-2)?
9. What is the value of (25^(3/4))^(-1/2)?
10. What is the value of (16^(3/4))^(-2/3)?

Complete the following table:

Simplify the following:

11. (2^(1/3) * 2^(2/3))^3
12. (x^(1/2) * x^(-1/2))^2
13. (5^(1/2) 5^(-1/2) 5^(1/2))^2
14. (2^(1/4) * 2^(-1/4))^3
15. (x^(1/2) x^(-1/2) x^(3/2))^2

Convert the following to radical form:

16. 2^(3/2)
17. 4^(1/3)
18. 5^(2/5)
19. 8^(3/4)
20. 16^(5/6)

Solve for x:

21. x^(3/4) = 81
22. x^(2/3) = 27
23. x^(1/2) = 2^(1/2)
24. x^(-3/4) = 16
25. x^(5/4) = 32

Convert the following to exponential form:

26. √2 = 2^(1/2)
27. ³√27 = 3
28. ⁴√16 = 2
29. ⁵√32 = 2
30. √(x^2) = x

Good luck!