\(\dfrac{[(\frac{3a}{4b})^{-3}]^2 }{ (\frac{16a^{-3}}{3b})^2} \\= \left[\left(\dfrac{4b}{3a}\right)^{3}\right]^2 \cdot \left(\dfrac{3b}{16a^{-3}}\right)^2 \\= \dfrac{ 4^6b^6\cdot 3^2b^2\cdot a^6 }{ 3^6 a^6 \cdot 16^2 } \\= \dfrac{ 4^6b^6 \cdot b^2}{ 3^4\cdot 4^4 } \\= \dfrac{ 4^2b^8}{ 81 }\\= \dfrac{ 16 b^8}{ 81} \)
