Sifat-sifat Exponen

$1.\,{{a}^{p}}\,+\,{{a}^{q}}\,=\,{{a}^{p+q}}$
$2.\,{{a}^{p}}:{{a}^{q}}\,=\,{{a}^{p-q}}$

$3.\,{{\left( a.b \right)}^{p}}\,=\,{{a}^{p}}.{{b}^{p}}$
$4.\,{{\left( a:b \right)}^{p}}\,=\,{{a}^{p}}:{{b}^{p}}$
$5.\,{{\left( {{a}^{p}} \right)}^{q}}\,=\,{{a}^{pq}}$
$6.\,{{a}^{-p}}\,=\,\frac{1}{{{a}^{p}}}$
$7.\,{{a}^{0}}\,=\,1\,,\,a\ne 0$
$8.\,{{a}^{\frac{p}{q}}}\,=\,\sqrt[q]{{{a}^{p}}}$
$9.\,{{a}^{2}}-{{b}^{2}}\,=\,\left( a-b \right)\left( a+b \right)$
$10.\,{{a}^{3}}-{{b}^{3}}\,=\,\left( a-b \right)\left( {{a}^{2}}+ab+{{b}^{2}} \right)$
$11.\,{{a}^{3}}+{{b}^{3}}\,=\,\left( a+b \right)\left( {{a}^{2}}-ab+{{b}^{2}} \right)$
$12.\,\sqrt[p]{a.b}\,=\,\sqrt[p]{a}.\sqrt[p]{b}$
$13.\,\sqrt[p]{\frac{a}{b}}\,=\,\frac{\sqrt[p]{a}}{\sqrt[p]{b}}$
$14.\,\sqrt{\left( a+b \right)+2\sqrt{ab}}\,=\,\sqrt{a}+\sqrt{b}$
$15.\,\sqrt{\left( a+b \right)-2\sqrt{ab}}\,=\,\sqrt{a}-\sqrt{b}\,,\,a>b$
$16.\,\frac{a}{b\sqrt{c}}x\frac{\sqrt{c}}{\sqrt{c}}\,=\,\frac{a}{bc}\sqrt{c}$
$17.\,\frac{a}{b\sqrt{c}+d\sqrt{e}}x\frac{b\sqrt{c}-d\sqrt{e}}{b\sqrt{c}-d\sqrt{e}}\,=\,a\left( \frac{b\sqrt{c}-d\sqrt{e}}{{{b}^{2}}c-{{d}^{2}}c} \right)$
$18.\,\frac{a}{b\sqrt{c}-d\sqrt{e}}x\frac{b\sqrt{c}+d\sqrt{e}}{b\sqrt{c}+d\sqrt{e}}\,=\,a\left( \frac{b\sqrt{c}+d\sqrt{e}}{{{b}^{2}}c-{{d}^{2}}c} \right)$