Question

Simplifique a expressão:

Answer 1

$\left (\sqrt[3]{ \sqrt[6]{2^9} } \right)^5\,\cdot\,\left( \sqrt[6]{ \sqrt[3]{2^9} } \right)^5$

$\left[\left (2^{ \frac{9}{6}} \right)^{ \frac{1}{3}\right]^5 \cdot \left[\left(2^ {\frac{9}{3}\right)^{ \frac{1}{6}}\right]^5 \\ \\ \\ \left(2^{ (\frac{9}{6}\cdot \frac{1}{3} \cdot5)\right)\cdot\left(2^{({ \frac{9}{3}\cdot \frac{1}{6}\cdot5)}\right) \\ \\ \\ 2^{ \frac{5}{2}}\cdot2^{ \frac{5}{2}} = 2^{ \frac{10}{2}} = 2^5 \rightarrow \boxed{=32}$