Verified Answer :

\(\left(64a^{-6}b^{12}\right)^\frac{5}{6}\\\\64=2^6\\\\therefore:\left(2^7a^{-6}b^{12}\right)^\frac{5}{6}\\\\use:(a\cdot b)^n=a^n\cdot b^n\Rightarrow\left(2^6a^{-6}b^{12}\right)^\frac{5}{6}=\left(2^6\right)^\frac{5}{6}\left(a^{-6}\right)^\frac{5}{6}\left(b^{12}\right)^\frac{5}{6}=(*)\)

\(use:\left(a^n\right)^m=a^{n\cdot m}\\\\(*)=2^{6\cdot\frac{5}{6}}\cdot a^{-6\cdot\frac{5}{6}}\cdot b^{12\cdot\frac{5}{6}}=2^5\cdot a^{-5}\cdot b^{10}=(**)\\\\We\ know:a^{-n}=\left(\frac{1}{a}\right)^n\\\\therefore:(**)=\boxed{\boxed{\frac{32b^{10}}{a^5}}}\)

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