Need to solve (1/2 L ^ -1/2) / (1/3 K ^-2/3) = 2/3?

Question

Must find K and L,

Answer 1

2 variables means you need two equations

Answer 2

(1/2 L ^ -1/2) / (1/3 K ^-2/3) = 2/3
I think you're saying:
((1/2)L^-1/2) / ((1/3)*K^-2/3) = 2/3
That is L and K are in denominators of the two fractions.

1/2 L^-1/2 = 1/(2sqrtL)
1/3 K^-2/3 = 1/(3sqrtK^3)
So the problem becomes 3sqrtK^3 / 2sqrtL = 2/3
or 9sqrtK^3 = 4sqrtL
One solution is L=81 and K=cuberoot16= 2cuberoot2

Answer 3

You have to do it in 2 different problems.

Isolate K and set L to zero. Then get the answer for K.

Next problem, isolate L and set K to zero.