# One-Step Exponent Law Practice

In this exercise you will practice with the exponent laws, all mixed-up.

These problems require only a
*single* application of a *single* exponent law.
For more advanced problems,
see Multi-Step Exponent Law Practice.

Let $\,x\,,$ $\,y\,,$ $\,m\,,$ and $\,n\,$ be real numbers, with the following exceptions:

- a base and exponent cannot simultaneously be zero (since $\,0^0\,$ is undefined);
- division by zero is not allowed;
- for non-integer exponents (like $\,\frac12\,$ or $\,0.4\,$), assume that bases are positive.

Then:

$x^mx^n = x^{m+n}$ | Verbalize: same base, things multiplied, add the exponents |

$\displaystyle \frac{x^m}{x^n} = x^{m-n}$ | Verbalize: same base, things divided, subtract the exponents |

$(x^m)^n = x^{mn}$ | Verbalize: something to a power, to a power; multiply the exponents |

$(xy)^m = x^my^m$ | Verbalize: product to a power; each factor gets raised to the power |

$\displaystyle \left(\frac{x}{y}\right)^m = \frac{x^m}{y^m}$ | Verbalize: fraction to a power; both numerator and denominator get raised to the power |