The answer is [tex]\frac{x^{4/3}y^{3}}{3} [/tex].
The fraction is: [tex] \frac{4xy^{-2} }{12 x^{-1/3} y^{-5} } [/tex]
Let's rewrite it: [tex]\frac{4xy^{-2} }{12 x^{-1/3} y^{-5} }=\frac{4 }{12 }*\frac{x }{ x^{-1/3} }*\frac{y^{-2} }{ y^{-5} }[/tex]
Since [tex] \frac{x^{a} }{x^{b}} =x^{a-b} [/tex],
then:
*** [tex]\frac{x}{ x^{-1/3} }= x^{1-(-1/3)} = x^{3/3+1/3} = x^{4/3} [/tex]
*** [tex]\frac{y^{-2} }{ y^{-5} }= y^{-2-(-5)} = y^{-2+5} = y^{3} [/tex]
______
[tex]\frac{4 }{12 }*\frac{x }{ x^{-1/3} }*\frac{y^{-2} }{ y^{-5} }= \frac{1*4}{3*4}* x^{4/3}*y^{3}= \frac{1}{3} * x^{4/3}*y^{3}= \frac{x^{4/3}y^{3}}{3} [/tex]
