simplificando ∜(5^(14 )-5^13)/20 , qual é o numero natural obtido?
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Os cálculos são simples
![\sqrt[4]{ \frac{5^{14}-5^{13}}{20} } \\
\\ \sqrt[4]{ \frac{5^{12}*5^2-5^{12}*5}{20} } \\
\\ \sqrt[4]{ \frac{5^{12}(25-5)}{20} }\\
\\ \sqrt[4]{5^{12}} \\
\\5^{ \frac{12}{4} }\\
\\\boxed{\boxed{\therefore~125}}](https://tex.z-dn.net/?f=+%5Csqrt%5B4%5D%7B+%5Cfrac%7B5%5E%7B14%7D-5%5E%7B13%7D%7D%7B20%7D+%7D+%5C%5C%0A%5C%5C+%5Csqrt%5B4%5D%7B+%5Cfrac%7B5%5E%7B12%7D%2A5%5E2-5%5E%7B12%7D%2A5%7D%7B20%7D+%7D+%5C%5C%0A%5C%5C+%5Csqrt%5B4%5D%7B+%5Cfrac%7B5%5E%7B12%7D%2825-5%29%7D%7B20%7D+%7D%5C%5C%0A%5C%5C+%5Csqrt%5B4%5D%7B5%5E%7B12%7D%7D+%5C%5C%0A%5C%5C5%5E%7B+%5Cfrac%7B12%7D%7B4%7D+%7D%5C%5C%0A%5C%5C%5Cboxed%7B%5Cboxed%7B%5Ctherefore%7E125%7D%7D+ "\sqrt[4]{ \frac{5^{14}-5^{13}}{20} } \\
\\ \sqrt[4]{ \frac{5^{12}*5^2-5^{12}*5}{20} } \\
\\ \sqrt[4]{ \frac{5^{12}(25-5)}{20} }\\
\\ \sqrt[4]{5^{12}} \\
\\5^{ \frac{12}{4} }\\
\\\boxed{\boxed{\therefore~125}}")
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