can someone solve 2000 = 4𝐾^0.75 * L^0.25 where k=3/10 L. i tryed to solve this by adding the powers 2000=4(3/10 L^1) however i get an answer of 5000/3 which is not the correct answer the correct answer is 5000(10/3)^.75
can someone solve 2000 = 4𝐾^0.75 * L^0.25 where k=3/10 L. i tryed to solve this by adding the powers 2000=4(3/10 L^1) however i get an answer of 5000/3 which is not the correct answer the correct answer is 5000(10/3)^.75
We are given to solve for $L$:
$ \displaystyle 2000=4K^{\frac{3}{4}}L^{\frac{1}{4}}$
Divide through by 4:
$ \displaystyle 500=K^{\frac{3}{4}}L^{\frac{1}{4}}$
We are told:
$ \displaystyle K=\frac{3}{10}L$:
$ \displaystyle 500=\left(\frac{3}{10}L\right)^{\frac{3}{4}}L^{\frac{1}{4}}=\left(\frac{3}{10}\right)^{\frac{3}{4}}L$
Hence:
$ \displaystyle L=500\left(\frac{10}{3}\right)^{\frac{3}{4}}$