Question

u=xy, v=x(y^4)
solve for x and y in terms of u and v

Answer 1

\[\large v = xy^4 \implies v = (xy) (y^3) \implies v = u(y^3)\]

So,
\[\large y^3 = \frac{v}{u} \implies y = \sqrt[3]{\frac{v}{u}}\]

This is the value of y..

For x:

\[\large u = xy \implies u^3 = x^3.y^3\]

\[\large u^3 = x^3(\frac{v}{u}) \implies u^4 = v.x^3\]

\[\large x^3 = \frac{u^4}{v} \implies x = \sqrt[3]{\frac{u^4}{v}} \implies x = u \sqrt[3]{\frac{u}{v}}\]