Замените степенью с целым отрицательным показателем дроби:
1) 1/81; 2) 1/64; 3) 1/121; 4) 1/625; 5) 1/841; 6) 1/256
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Вспомним свойство степеней
![displaystyle frac{1}{x^n}=x^{-n} displaystyle frac{1}{x^n}=x^{-n}](https://tex.z-dn.net/?f=displaystyle++frac%7B1%7D%7Bx%5En%7D%3Dx%5E%7B-n%7D+)
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![displaystyle frac{1}{81}= frac{1}{9^2}= frac{1}{(3^2)^2}= frac{1}{3^4} \\ frac{1}{81}=9^{-2}=3^{-4} displaystyle frac{1}{81}= frac{1}{9^2}= frac{1}{(3^2)^2}= frac{1}{3^4} \\ frac{1}{81}=9^{-2}=3^{-4}](https://tex.z-dn.net/?f=displaystyle++frac%7B1%7D%7B81%7D%3D+frac%7B1%7D%7B9%5E2%7D%3D+frac%7B1%7D%7B%283%5E2%29%5E2%7D%3D+frac%7B1%7D%7B3%5E4%7D++++%5C%5C+frac%7B1%7D%7B81%7D%3D9%5E%7B-2%7D%3D3%5E%7B-4%7D)
![displaystyle frac{1}{64}= frac{1}{8^2}= frac{1}{(2^3)^2}= frac{1}{2^6}= frac{1}{(2^2)^3}= frac{1}{4^3} \\ frac{1}{64}=8^{-2}=4^{-3}=2^{-6} displaystyle frac{1}{64}= frac{1}{8^2}= frac{1}{(2^3)^2}= frac{1}{2^6}= frac{1}{(2^2)^3}= frac{1}{4^3} \\ frac{1}{64}=8^{-2}=4^{-3}=2^{-6}](https://tex.z-dn.net/?f=displaystyle++frac%7B1%7D%7B64%7D%3D+frac%7B1%7D%7B8%5E2%7D%3D+frac%7B1%7D%7B%282%5E3%29%5E2%7D%3D+frac%7B1%7D%7B2%5E6%7D%3D+frac%7B1%7D%7B%282%5E2%29%5E3%7D%3D+frac%7B1%7D%7B4%5E3%7D+%5C%5C+frac%7B1%7D%7B64%7D%3D8%5E%7B-2%7D%3D4%5E%7B-3%7D%3D2%5E%7B-6%7D+++++)
![displaystyle frac{1}{121}= frac{1}{11^2}\\ frac{1}{121}=11^{-2} displaystyle frac{1}{121}= frac{1}{11^2}\\ frac{1}{121}=11^{-2}](https://tex.z-dn.net/?f=displaystyle++frac%7B1%7D%7B121%7D%3D+frac%7B1%7D%7B11%5E2%7D%5C%5C+frac%7B1%7D%7B121%7D%3D11%5E%7B-2%7D+++)
![displaystyle frac{1}{625}= frac{1}{25^2}= frac{1}{(5^2)^2}= frac{1}{5^4} \\ frac{1}{625}=25^{-2}=5^{-4} displaystyle frac{1}{625}= frac{1}{25^2}= frac{1}{(5^2)^2}= frac{1}{5^4} \\ frac{1}{625}=25^{-2}=5^{-4}](https://tex.z-dn.net/?f=displaystyle++frac%7B1%7D%7B625%7D%3D+frac%7B1%7D%7B25%5E2%7D%3D+frac%7B1%7D%7B%285%5E2%29%5E2%7D%3D+frac%7B1%7D%7B5%5E4%7D+%5C%5C+frac%7B1%7D%7B625%7D%3D25%5E%7B-2%7D%3D5%5E%7B-4%7D++++)
![displaystyle frac{1}{841}= frac{1}{29^2}=29^{-2} displaystyle frac{1}{841}= frac{1}{29^2}=29^{-2}](https://tex.z-dn.net/?f=displaystyle++frac%7B1%7D%7B841%7D%3D++frac%7B1%7D%7B29%5E2%7D%3D29%5E%7B-2%7D+)
![displaystyle frac{1}{256}= frac{1}{16^2}= frac{1}{(4^2)^2}= frac{1}{4^4}= frac{1}{(2^2)^4}= frac{1}{2^8}\\ frac{1}{256}=16^{-2}=4^{-4}=2^{-8} displaystyle frac{1}{256}= frac{1}{16^2}= frac{1}{(4^2)^2}= frac{1}{4^4}= frac{1}{(2^2)^4}= frac{1}{2^8}\\ frac{1}{256}=16^{-2}=4^{-4}=2^{-8}](https://tex.z-dn.net/?f=displaystyle++frac%7B1%7D%7B256%7D%3D++frac%7B1%7D%7B16%5E2%7D%3D+frac%7B1%7D%7B%284%5E2%29%5E2%7D%3D+frac%7B1%7D%7B4%5E4%7D%3D+frac%7B1%7D%7B%282%5E2%29%5E4%7D%3D+frac%7B1%7D%7B2%5E8%7D%5C%5C++frac%7B1%7D%7B256%7D%3D16%5E%7B-2%7D%3D4%5E%7B-4%7D%3D2%5E%7B-8%7D+++)
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