Question

Simplify (4xy^-2)/(12x^(-1/3)y^-5) and Show work ...?

Answer 1

The answer is $\frac{x^{4/3}y^{3}}{3}$.

The fraction is: $\frac{4xy^{-2} }{12 x^{-1/3} y^{-5} }$
Let's rewrite it: $\frac{4xy^{-2} }{12 x^{-1/3} y^{-5} }=\frac{4 }{12 }*\frac{x }{ x^{-1/3} }*\frac{y^{-2} }{ y^{-5} }$

Since $\frac{x^{a} }{x^{b}} =x^{a-b}$,
then:
*** $\frac{x}{ x^{-1/3} }= x^{1-(-1/3)} = x^{3/3+1/3} = x^{4/3}$
*** $\frac{y^{-2} }{ y^{-5} }= y^{-2-(-5)} = y^{-2+5} = y^{3}$
______
$\frac{4 }{12 }*\frac{x }{ x^{-1/3} }*\frac{y^{-2} }{ y^{-5} }= \frac{1*4}{3*4}* x^{4/3}*y^{3}= \frac{1}{3} * x^{4/3}*y^{3}= \frac{x^{4/3}y^{3}}{3}$