a is negative |
a is zero |
a is positive |

a^{n} is negative |
a^{n} is zero |
a^{n} is positive |

b is negative |
b is zero |
b is positive |

one real solution, negative | one real solution, zero | one real solution, positive |

^{n}√*b*=*a*;*a*^{n}=*b*.

b is negative |
b is zero |
b is positive |

^{n}√b
is negative |
^{n}√b
is zero |
^{n}√b
is positive |

a is negative |
a is zero |
a is positive |

a^{n} is positive |
a^{n} is zero |
a^{n} is positive |

b is negative |
b is zero |
b is positive |

no real solution | one real solution, zero | two real solutions, one negative and one positive |

^{n}√*b*=*a*;*a*^{n}=*b*, and*a*≥ 0.

b is negative |
b is zero |
b is positive |

^{n}√b
is imaginary |
^{n}√b
is zero |
^{n}√b
is positive |

Ifb^{m/n}=^{n}√(b^{m}).

Go back to the course homepage.

This web page was written between 2010 and 2015 by Toby Bartels, last edited on 2015 July 27. Toby reserves no legal rights to it. The permanent URI of this web page is

`http://tobybartels.name/MATH-1100/2015ss/roots/`

.