Formulas of Exponent and Power

$1.  {{a}^{n}}=a\times a\times a\times ...ntimes $

   ${{2}^{3}}=2\times 2\times 2=8 $

$2.  {{a}^{m}}\times {{a}^{n}}={{a}^{m+n}}$

   ${{3}^{2}}\times {{3}^{3}}={{3}^{2+3}}={{3}^{5}}=243$

$3.  {{a}^{m}}\div {{a}^{n}}={{a}^{m-n}}$

   ${{5}^{4}}\div {{5}^{1}}={{5}^{4-1}}={{5}^{3}}=125$

$4.  {{({{a}^{m}})}^{n}}={{a}^{mn}}$

   ${{({{2}^{3}})}^{2}}={{2}^{3\times 2}}={{2}^{6}}=64$

$5.  {{(ab)}^{n}}={{a}^{n}}{{b}^{n}}$

   ${{(5x)}^{2}}={{5}^{2}}{{x}^{2}}=25{{x}^{2}}$


$6.  {{(\frac{a}{b})}^{n}}=\frac{{{a}^{n}}}{{{b}^{n}}}$

   ${{(\frac{2}{3})}^{3}}=\frac{{{2}^{3}}}{{{3}^{3}}}=\frac{8}{27}$

$7.  {{a}^{1}}=a$

   ${{6}^{1}}=6$

$8.  {{a}^{0}}=1 $

   ${{45}^{0}}=1$


$9.  {{a}^{-n}}=\frac{1}{{{a}^{n}}}$

   ${{5}^{-2}}=\frac{1}{{{5}^{2}}}=\frac{1}{25}$

$10.  {{(\frac{a}{b})}^{-n}}=\frac{{{a}^{-n}}}{{{b}^{-n}}}=\frac{{{b}^{n}}}{{{a}^{n}}}$

    ${{(\frac{4}{7})}^{-2}}=\frac{{{4}^{-2}}}{{{7}^{-2}}}=\frac{{{7}^{2}}}{{{4}^{2}}}=\frac{49}{16}$

$11.   \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$

   $\sqrt{\frac{25}{64}}=\frac{\sqrt{25}}{\sqrt{64}}=\frac{5}{8}$


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