Question

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

Answer 1

The answer is
`(x^(4/3)y^(3))/(3)`.

The fraction is:
`(4xy^(-2) )/(12 x^(-1/3) y^(-5) )`
Let's rewrite it:
`(4xy^(-2) )/(12 x^(-1/3) y^(-5) )=(4 )/(12 )*(x )/( x^(-1/3) )*(y^(-2) )/( y^(-5) )`

Since
`(x^(a) )/(x^(b)) =x^(a-b)`,
then:
***
`(x)/( x^(-1/3) )= x^(1-(-1/3)) = x^(3/3+1/3) = x^(4/3)`
***
`(y^(-2) )/( y^(-5) )= y^(-2-(-5)) = y^(-2+5) = y^(3)`
______

`(4 )/(12 )*(x )/( x^(-1/3) )*(y^(-2) )/( y^(-5) )= (1*4)/(3*4)* x^(4/3)*y^(3)= (1)/(3) * x^(4/3)*y^(3)= (x^(4/3)y^(3))/(3)`