Exponent Laws

From RaVPup's Notes

There are six exponent laws that should be followed when manipulating terms in the $\mathbb{R}$ field. These six rules are as follows.

$x^mx^n=x^{m+n} \$

$\frac{x^m} {x^n}=x^{m-n} \$

$(x^m)^n = x^{mn} \$

$x^0 = 1 \mbox{ where } x \ne 0 \$

The case where $00$ is 1 by definition but cannot be derived from any of the rules of mathematics.

$\left( xy \right)^m = x^my^m \$

$\left( \frac{x}{y} \right)^m = \frac{x^m} {y^m} \$

$x^{-m} = \frac {1} {x^m} \$

$\left( \frac{x}{y} \right)^{-m} = \left( \frac{y} {x} \right)^m \$

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