# Negative Exponents

You can think of a negative exponent as one that's been "misplaced" and needs to be moved back onto the correct side of its fraction. So if I gave you *x*^{-2}, simplifying the expression is a matter of moving the exponent part from the numerator to the denominator and making the exponent positive so

x^{-2} = |
1 |

x^{2} |

Similary, if you had an exponent in the denominator, it would move to the numerator.

1 | = y^{3} |

y^{-3} |

Just like any other exponent simplification problem you should always be very wary of addition. If I asked you to simplify

x^{2} + y^{2} |

y^{-3} |

the correct answer would be

*y*^{3}(*x*^{2} + *y*^{2})

The denominator is being divided into *the entire numerator* so when you "fix" the negative exponent, you have to apply it to the entire numerator, not just, for example, the *y* part or the *x* part