# Equations » Power equations

A power formula is always of the form `y` = `ax ^{b}`.

A power equation is always of the form

`ax`=

^{b}`c`.

### One or two solutions?

A power equation always has one solution when you have an odd exponent.

A power equation has two, one or zero solutions when you have an even exponent.

Think of a quadratic equation (even exponent):

`x`^{2} = 4 has two solutions, namely `x` = –2 or `x` = 2.

`x`^{2} = 0 has one solution, namely `x` = 0.

`x`^{2} = –1 has no solutions.

### Root = power

Every root can be written as a power.The rule is =

`x`

^{}.

*Example 1*

3x^{4} + 8 | = 1883 |

3x^{4} | = 1875 |

x^{4} | = 625 |

x = – | of x = |

x = –5 | or x = 5 |

*Example 2*

500 – 2x^{5} | = 14 |

2x^{5} | = 486 |

x^{5} | = 243 |

x | = = 3 |

*Example 3*

7x^{3} + 6 | = –204 |

7x^{3} | = –210 |

x^{3} | = –30 |

x | = ≈ –3.107 |

*Example 4*

On the graph of `y` = 112`x`^{0.43} lies point (`x`; 14.5).

Calculate `x`. Round to 4 decimals.

Answer:

14.5 = | 112x^{0.43} |

x^{0.43} = | 14.5112 |

x = | 14.5112 ≈ 0.0086 |