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