(6√5^10/3√5^2)^4 como resolver essa expressão?
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Lembrete:
๏![\mathsf{\sqrt[b]{a^c}=a^{\frac{c}{b}}}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Csqrt%5Bb%5D%7Ba%5Ec%7D%3Da%5E%7B%5Cfrac%7Bc%7D%7Bb%7D%7D%7D "\mathsf{\sqrt[b]{a^c}=a^{\frac{c}{b}}}")
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Resolução:
![\mathsf{\left[\dfrac{\left(\sqrt[6]{5}\right)^{10}}{\left(\sqrt[3]{5}\right)^2}\right]^4}\\\\\\\mathsf{\dfrac{\left(\sqrt[6]{5}\right)^{40}}{\left(\sqrt[3]{5}\right)^8}}\\\\\\\mathsf{\dfrac{5^{\frac{40}{6}}}{5^{\frac{8}{3}}}}\\\\\\\mathsf{5^{\left(\frac{40}{6}-\frac{8}{3}\right)}}\\\\\mathsf{5^{\left(\frac{40-16}{6}\right)}}\\\\\mathsf{5^{\left(\frac{24}{6}\right)}}\\\\\mathsf{5^4}\\\\\boxed{\boxed{\mathsf{625}}}\: \: \checkmark](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cleft%5B%5Cdfrac%7B%5Cleft%28%5Csqrt%5B6%5D%7B5%7D%5Cright%29%5E%7B10%7D%7D%7B%5Cleft%28%5Csqrt%5B3%5D%7B5%7D%5Cright%29%5E2%7D%5Cright%5D%5E4%7D%5C%5C%5C%5C%5C%5C%5Cmathsf%7B%5Cdfrac%7B%5Cleft%28%5Csqrt%5B6%5D%7B5%7D%5Cright%29%5E%7B40%7D%7D%7B%5Cleft%28%5Csqrt%5B3%5D%7B5%7D%5Cright%29%5E8%7D%7D%5C%5C%5C%5C%5C%5C%5Cmathsf%7B%5Cdfrac%7B5%5E%7B%5Cfrac%7B40%7D%7B6%7D%7D%7D%7B5%5E%7B%5Cfrac%7B8%7D%7B3%7D%7D%7D%7D%5C%5C%5C%5C%5C%5C%5Cmathsf%7B5%5E%7B%5Cleft%28%5Cfrac%7B40%7D%7B6%7D-%5Cfrac%7B8%7D%7B3%7D%5Cright%29%7D%7D%5C%5C%5C%5C%5Cmathsf%7B5%5E%7B%5Cleft%28%5Cfrac%7B40-16%7D%7B6%7D%5Cright%29%7D%7D%5C%5C%5C%5C%5Cmathsf%7B5%5E%7B%5Cleft%28%5Cfrac%7B24%7D%7B6%7D%5Cright%29%7D%7D%5C%5C%5C%5C%5Cmathsf%7B5%5E4%7D%5C%5C%5C%5C%5Cboxed%7B%5Cboxed%7B%5Cmathsf%7B625%7D%7D%7D%5C%3A+%5C%3A+%5Ccheckmark "\mathsf{\left[\dfrac{\left(\sqrt[6]{5}\right)^{10}}{\left(\sqrt[3]{5}\right)^2}\right]^4}\\\\\\\mathsf{\dfrac{\left(\sqrt[6]{5}\right)^{40}}{\left(\sqrt[3]{5}\right)^8}}\\\\\\\mathsf{\dfrac{5^{\frac{40}{6}}}{5^{\frac{8}{3}}}}\\\\\\\mathsf{5^{\left(\frac{40}{6}-\frac{8}{3}\right)}}\\\\\mathsf{5^{\left(\frac{40-16}{6}\right)}}\\\\\mathsf{5^{\left(\frac{24}{6}\right)}}\\\\\mathsf{5^4}\\\\\boxed{\boxed{\mathsf{625}}}\: \: \checkmark")
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Resolução:
Rodrigo2679:
Vlw mas esse 3 e 6 são índices da raiz
N são multiplicação
Pronto, editei.
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