# Worksheet Test

Answer the following questions:

- What is the value of 2^(1/2)?
- What is the value of 4^(1/3)?
- What is the value of 8^(2/3)?
- What is the value of 16^(1/4)?
- What is the value of 10^(1/2) * 10^(1/4)?
- What is the value of (27^(1/3))^2?
- What is the value of (2^(1/2))^3?
- What is the value of (3^(1/3))^(-2)?
- What is the value of (25^(3/4))^(-1/2)?
- 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:

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

Convert the following to radical form:

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

Solve for x:

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

Convert the following to exponential form:

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

Good luck!