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Verified Answer :

\(ba^4\cdot(2ba^4)^{-3}=\dfrac{ba^4}{(2ba^4)^3}=\dfrac{ba^4}{8b^3a^{12}}=\dfrac{1}{8b^2a^8}\)

\(a^{4}b(2ab^{4})^{-3}\)

\(a^{4}b( \frac{1}{(2a^{4}b)^{3}})\)

\(a^{4}b( \frac{1}{(2a^{4}b)(2a^{4}b)(2a^{4}b)})\)

\(a^{4}b( \frac{1}{8a^{12}b^{3}})\)

\(\frac{1}{8a^{8}b^{2}}\)