Sifat-sifat Exponen

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

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