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( 27 1 ) 5 2 ( 3 1 ) − 3 2 ÷ ( 81 1 ) 3 2 ( 9 1 ) 12 5 = ...

$\frac{( \frac{1}{3} ) ^{- \frac{2}{3}}}{( \frac{1}{27} ) ^{\frac{2}{5}}} \div \frac{( \frac{1}{9} ) ^{\frac{5}{12}}}{( \frac{1}{81} ) ^{\frac{2}{3}}} =$ ...

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open parentheses begin display style 1 third end style close parentheses to the power of negative begin display style 2 over 3 end style end exponent over open parentheses begin display style 1 over 27 end style close parentheses to the power of begin display style 2 over 5 end style end exponent divided by open parentheses begin display style 1 over 9 end style close parentheses to the power of begin display style 5 over 12 end style end exponent over open parentheses begin display style 1 over 81 end style close parentheses to the power of begin display style 2 over 3 end style end exponent

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$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses begin display style 1 third end style close parentheses to the power of negative begin display style 2 over 3 end style end exponent over open parentheses begin display style 1 over 27 end style close parentheses to the power of begin display style 2 over 5 end style end exponent divided by open parentheses begin display style 1 over 9 end style close parentheses to the power of begin display style 5 over 12 end style end exponent over open parentheses begin display style 1 over 81 end style close parentheses to the power of begin display style 2 over 3 end style end exponent end cell equals cell left parenthesis 3 to the power of negative 1 end exponent right parenthesis to the power of negative begin display style 2 over 3 end style end exponent over open parentheses begin display style 1 over 3 cubed end style close parentheses to the power of begin display style 2 over 5 end style end exponent divided by open parentheses begin display style 1 over 3 squared end style close parentheses to the power of begin display style 5 over 12 end style end exponent over open parentheses begin display style 1 over 3 to the power of 4 end style close parentheses to the power of begin display style 2 over 3 end style end exponent end cell row blank equals cell 3 to the power of begin display style 2 over 3 end style end exponent over left parenthesis 3 to the power of negative 3 end exponent right parenthesis to the power of begin display style 2 over 5 end style end exponent divided by left parenthesis 3 to the power of negative 2 end exponent right parenthesis to the power of begin display style 5 over 12 end style end exponent over left parenthesis 3 to the power of negative 4 end exponent right parenthesis to the power of begin display style 2 over 3 end style end exponent end cell row blank equals cell 3 to the power of begin display style 2 over 3 end style end exponent over 3 to the power of begin display style negative 6 over 5 end style end exponent divided by 3 to the power of negative begin display style 5 over 6 end style end exponent over 3 to the power of negative begin display style 8 over 3 end style end exponent end cell row blank equals cell 3 to the power of begin display style 2 over 3 end style end exponent over 3 to the power of begin display style negative 6 over 5 end style end exponent cross times 3 to the power of negative begin display style 8 over 3 end style end exponent over 3 to the power of negative begin display style 5 over 6 end style end exponent end cell row blank equals cell 3 to the power of 2 over 3 plus open parentheses negative 8 over 3 close parentheses end exponent divided by 3 to the power of negative 6 over 5 plus open parentheses negative 5 over 6 close parentheses end exponent end cell row blank equals cell 3 to the power of negative 2 end exponent divided by 3 to the power of negative 61 over 30 end exponent end cell row blank equals cell 3 to the power of negative 2 minus open parentheses negative 61 over 30 close parentheses end exponent end cell row blank equals cell 3 to the power of fraction numerator negative 60 plus 61 over denominator 30 end fraction end exponent end cell row blank equals cell 3 to the power of 1 over 30 end exponent end cell end table$

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