Question

(6√5^10/3√5^2)^4 como resolver essa expressão?

Answer 1

Lembrete:

๏ $\mathsf{\sqrt[b]{a^c}=a^{\frac{c}{b}}}$
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Resolução:

$\mathsf{\left[\dfrac{\left(\sqrt[6]{5}\right)^{10}}{\left(\sqrt[3]{5}\right)^2}\right]^4}\\\\\\\mathsf{\dfrac{\left(\sqrt[6]{5}\right)^{40}}{\left(\sqrt[3]{5}\right)^8}}\\\\\\\mathsf{\dfrac{5^{\frac{40}{6}}}{5^{\frac{8}{3}}}}\\\\\\\mathsf{5^{\left(\frac{40}{6}-\frac{8}{3}\right)}}\\\\\mathsf{5^{\left(\frac{40-16}{6}\right)}}\\\\\mathsf{5^{\left(\frac{24}{6}\right)}}\\\\\mathsf{5^4}\\\\\boxed{\boxed{\mathsf{625}}}\: \: \checkmark$