The answer is \(\frac{a^{6}}{b^{5}}\)
The expression is: \(\frac{ a^{2} b^{-3} }{ a^{-4} b^{2} }\)
Using the rule: \(\frac{ x^{a} }{ x^{b} }= x^{a-b}\), we can rewrite the expression: \(\frac{ a^{2} b^{-3} }{ a^{-4} b^{2} }=a^{2-(-4)}b^{-3-2}= a^{2+4} b^{-5} =a^{6} b^{-5}\)
Using the rule: \(x^{-a} = \frac{1}{ x^{a} }\), we can rewrite \(a^{6} b^{-5}\): \(a^{6} b^{-5}= \frac{a^{6}}{b^{5}}\)
