[tex]\frac{(5x)^{-4}}{ x^{-9}} = \frac{ \frac{1}{(5x)^{ 4}}}{ \frac{1}{x^{ 9 }}} =\frac{5}{x^4} :\frac{1}{x^{9}} =\frac{1}{625x^4} \cdot \frac{x^{9}}{1} = \frac{ x^{9}}{625x^{4}}= \frac{ x^{9-4}}{625 }= \frac{x^5}{625} \\\\or\\\\\frac{5x^{-4}}{ x^{-9}} = \frac{5\cdot \frac{1}{x^{ 4}}}{ \frac{1}{x^{ 9 }}} =\frac{5}{x^4} :\frac{1}{x^{9}} =\frac{5}{x^4} \cdot \frac{x^{9}}{1} = \frac{5x^{9}}{x^{4}}=5x^{9-4}=5x^5
[/tex]
