Simplify \( \left(\frac{a^{-3} b}{c^{2}}\right)^{-4} \cdot\left(\frac{c^{5}}{a^{4} b^{-3}}\right)^{-1} \)

Calculate or simplify the expression \( ((a^{-3}b)/(c^{2}))^{-4} * ((c^{5})/(a^{4}b^{-3}))^{-1} \). Simplify the expression by following steps: - step0: Solution: \(\left(\frac{\left(a^{-3}b\right)}{\left(c^{2}\right)}\right)^{-4}\left(\frac{\left(c^{5}\right)}{\left(a^{4}b^{-3}\right)}\right)^{-1}\) - step1: Evaluate: \(\left(\frac{\left(a^{-3}b\right)}{c^{2}}\right)^{-4}\left(\frac{c^{5}}{\left(a^{4}b^{-3}\right)}\right)^{-1}\) - step2: Remove the parentheses: \(\left(\frac{a^{-3}b}{c^{2}}\right)^{-4}\left(\frac{c^{5}}{a^{4}b^{-3}}\right)^{-1}\) - step3: Rewrite the expression: \(\left(\frac{b}{a^{3}c^{2}}\right)^{-4}\left(\frac{c^{5}}{a^{4}b^{-3}}\right)^{-1}\) - step4: Rewrite the expression: \(\left(\frac{b}{a^{3}c^{2}}\right)^{-4}\left(\frac{b^{3}c^{5}}{a^{4}}\right)^{-1}\) - step5: Rewrite the expression: \(\frac{a^{12}c^{8}}{b^{4}}\times \frac{a^{4}}{b^{3}c^{5}}\) - step6: Reduce the numbers: \(\frac{a^{12}c^{3}}{b^{4}}\times \frac{a^{4}}{b^{3}}\) - step7: Multiply the terms: \(\frac{a^{12}c^{3}a^{4}}{b^{4}\times b^{3}}\) - step8: Multiply the terms: \(\frac{a^{16}c^{3}}{b^{4}\times b^{3}}\) - step9: Multiply the terms: \(\frac{a^{16}c^{3}}{b^{7}}\) The simplified expression is \( \frac{a^{16}c^{3}}{b^{7}} \).