 Date: May 14, 2023   # Worksheet Test

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:

Base Exponent Result
2 1/2
4 1/3
8 2/3
16 1/4
10 1/2
10 1/4
27 1/3
2 1/2
3 -1/3
25 3/4
16 3/4

Simplify the following:

1. (2^(1/3) * 2^(2/3))^3
2. (x^(1/2) * x^(-1/2))^2
3. (5^(1/2) 5^(-1/2) 5^(1/2))^2
4. (2^(1/4) * 2^(-1/4))^3
5. (x^(1/2) x^(-1/2) x^(3/2))^2

Convert the following to radical form:

1. 2^(3/2)
2. 4^(1/3)
3. 5^(2/5)
4. 8^(3/4)
5. 16^(5/6)

Solve for x:

1. x^(3/4) = 81
2. x^(2/3) = 27
3. x^(1/2) = 2^(1/2)
4. x^(-3/4) = 16
5. x^(5/4) = 32

Convert the following to exponential form:

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

Good luck!