Answer
$\frac{32}{9}\frac{b^{26}}{c^2}$
Work Step by Step
$(2b^4c^{-2})^5 (3b^{-3}c^{-4})^{-2}$
$=2^5 (b^4)^5(c^{-2})^5 3^{-2} (b^{-3})^{-2}(c^{-4})^{-2}$
$=32b^{20} c^{-10}\cdot \frac{1}{3^2}b^6 c^8$
$=\frac{32}{9} (b^{20}b^6)(c^{-10}c^8)$
$=\frac{32}{9}b^{26} c^{-2}$
$=\frac{32}{9}\frac{b^{26}}{c^2}$
