Usuń niewymierność z mianownika ułamka:
![a) \ \frac{1}{ \sqrt[n]{11}} \\ b) \ \frac{9^n-1}{ \sqrt[3n+1]{9}}](https://tex.z-dn.net/?f=a%29+%5C+%5Cfrac%7B1%7D%7B+%5Csqrt%5Bn%5D%7B11%7D%7D+%5C%5C++b%29+%5C+%5Cfrac%7B9%5En-1%7D%7B+%5Csqrt%5B3n%2B1%5D%7B9%7D%7D+ "a) \ \frac{1}{ \sqrt[n]{11}} \\ b) \ \frac{9^n-1}{ \sqrt[3n+1]{9}}")
MrPolygon
![a)\\{}\dfrac{1}{\sqrt[n]{11}}=\dfrac{1}{11^{\frac{1}{n}}}=\dfrac{1\cdot11^{\frac{n-1}{n}}}{11^{\frac{1}{n}}\cdot11^{\frac{n-1}{n}}}=\dfrac{11^{\frac{n-1}{n}}}{11^{\frac{n}{n}}}=\dfrac{\sqrt[n]{11^{n-1}}}{11}\\\\{}\\\\b)\\{}\dfrac{9^n-1}{\sqrt[3n+1]{9}}=\dfrac{9^n-1}{9^{\frac{1}{3n+1}}}=\dfrac{(9^n-1)\cdot9^{\frac{3n}{3n+1}}}{9^{\frac{1}{3n+1}}\cdot9^{\frac{3n}{3n+1}}}=\dfrac{(9^n-1)\cdot9^{\frac{3n}{3n+1}}}{9^{\frac{3n+1}{3n+1}}}=\\{}\\\\=\dfrac{(9^n-1)\cdot9^{\frac{3n}{3n+1}}}{9}](https://tex.z-dn.net/?f=a%29%5C%5C%7B%7D%5Cdfrac%7B1%7D%7B%5Csqrt%5Bn%5D%7B11%7D%7D%3D%5Cdfrac%7B1%7D%7B11%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D%7D%3D%5Cdfrac%7B1%5Ccdot11%5E%7B%5Cfrac%7Bn-1%7D%7Bn%7D%7D%7D%7B11%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D%5Ccdot11%5E%7B%5Cfrac%7Bn-1%7D%7Bn%7D%7D%7D%3D%5Cdfrac%7B11%5E%7B%5Cfrac%7Bn-1%7D%7Bn%7D%7D%7D%7B11%5E%7B%5Cfrac%7Bn%7D%7Bn%7D%7D%7D%3D%5Cdfrac%7B%5Csqrt%5Bn%5D%7B11%5E%7Bn-1%7D%7D%7D%7B11%7D%5C%5C%5C%5C%7B%7D%5C%5C%5C%5Cb%29%5C%5C%7B%7D%5Cdfrac%7B9%5En-1%7D%7B%5Csqrt%5B3n%2B1%5D%7B9%7D%7D%3D%5Cdfrac%7B9%5En-1%7D%7B9%5E%7B%5Cfrac%7B1%7D%7B3n%2B1%7D%7D%7D%3D%5Cdfrac%7B%289%5En-1%29%5Ccdot9%5E%7B%5Cfrac%7B3n%7D%7B3n%2B1%7D%7D%7D%7B9%5E%7B%5Cfrac%7B1%7D%7B3n%2B1%7D%7D%5Ccdot9%5E%7B%5Cfrac%7B3n%7D%7B3n%2B1%7D%7D%7D%3D%5Cdfrac%7B%289%5En-1%29%5Ccdot9%5E%7B%5Cfrac%7B3n%7D%7B3n%2B1%7D%7D%7D%7B9%5E%7B%5Cfrac%7B3n%2B1%7D%7B3n%2B1%7D%7D%7D%3D%5C%5C%7B%7D%5C%5C%5C%5C%3D%5Cdfrac%7B%289%5En-1%29%5Ccdot9%5E%7B%5Cfrac%7B3n%7D%7B3n%2B1%7D%7D%7D%7B9%7D "a)\\{}\dfrac{1}{\sqrt[n]{11}}=\dfrac{1}{11^{\frac{1}{n}}}=\dfrac{1\cdot11^{\frac{n-1}{n}}}{11^{\frac{1}{n}}\cdot11^{\frac{n-1}{n}}}=\dfrac{11^{\frac{n-1}{n}}}{11^{\frac{n}{n}}}=\dfrac{\sqrt[n]{11^{n-1}}}{11}\\\\{}\\\\b)\\{}\dfrac{9^n-1}{\sqrt[3n+1]{9}}=\dfrac{9^n-1}{9^{\frac{1}{3n+1}}}=\dfrac{(9^n-1)\cdot9^{\frac{3n}{3n+1}}}{9^{\frac{1}{3n+1}}\cdot9^{\frac{3n}{3n+1}}}=\dfrac{(9^n-1)\cdot9^{\frac{3n}{3n+1}}}{9^{\frac{3n+1}{3n+1}}}=\\{}\\\\=\dfrac{(9^n-1)\cdot9^{\frac{3n}{3n+1}}}{9}")
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