Demuestra que el exponente final de 5 en la expresión es 11
CarlGauss
Comprobación.
![( \sqrt{25 \sqrt[4]{ 5^{-3} \sqrt{5} } } )^{16}](https://tex.z-dn.net/?f=%28+%5Csqrt%7B25+%5Csqrt%5B4%5D%7B+5%5E%7B-3%7D+%5Csqrt%7B5%7D+%7D+%7D+%29%5E%7B16%7D+ "( \sqrt{25 \sqrt[4]{ 5^{-3} \sqrt{5} } } )^{16}")
![( \sqrt{25 \sqrt[4]{ \sqrt{5* 5^{-6} } } } )^{16}](https://tex.z-dn.net/?f=%28+%5Csqrt%7B25+%5Csqrt%5B4%5D%7B+%5Csqrt%7B5%2A+5%5E%7B-6%7D+%7D+%7D+%7D+%29%5E%7B16%7D+ "( \sqrt{25 \sqrt[4]{ \sqrt{5* 5^{-6} } } } )^{16}")
![( \sqrt{25 \sqrt[8]{5* 5^{-6} } } )^{16}](https://tex.z-dn.net/?f=+%28+%5Csqrt%7B25+%5Csqrt%5B8%5D%7B5%2A+5%5E%7B-6%7D+%7D+%7D+%29%5E%7B16%7D+ "( \sqrt{25 \sqrt[8]{5* 5^{-6} } } )^{16}")
![( \sqrt{ \sqrt[8]{5^{16} *5* 5^{-6} } ) } ^{16}](https://tex.z-dn.net/?f=+%28+%5Csqrt%7B++%5Csqrt%5B8%5D%7B5%5E%7B16%7D+%2A5%2A+5%5E%7B-6%7D+%7D+%29++%7D+%5E%7B16%7D+ "( \sqrt{ \sqrt[8]{5^{16} *5* 5^{-6} } ) } ^{16}")
![( \sqrt[16]{ 5^{11} } )^{16}](https://tex.z-dn.net/?f=+%28+%5Csqrt%5B16%5D%7B+5%5E%7B11%7D+%7D+%29%5E%7B16%7D+ "( \sqrt[16]{ 5^{11} } )^{16}")
![\sqrt[16]{ 5^{176} } = 5^{11}](https://tex.z-dn.net/?f=+%5Csqrt%5B16%5D%7B+5%5E%7B176%7D+%7D+%3D++5%5E%7B11%7D+ "\sqrt[16]{ 5^{176} } = 5^{11}")
<--- resultado.
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