Simplify: \(\left(\frac{\sqrt[3]{4096}}{\sqrt[4]{10000}}\right) \times \frac{5}{48} \times 186\).
31
Evaluate the cube root: \(\sqrt[3]{4096} = 16\), since \(16^3 = 4096\).
Evaluate the fourth root: \(\sqrt[4]{10000} = 10\), since \(10^4 = 10000\).
So the expression becomes \(\frac{16}{10} \times \frac{5}{48} \times 186\).
Simplifying: \(\frac{16}{10} \times \frac{5}{48} = \frac{80}{480} = \frac{1}{6}\).
Then \(\frac{1}{6} \times 186 = 31\).
Hence, the simplified value is 31.
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