Question

how does 1000/(pi(500/pi)^(2/3)=2(500/pi)^1/3

Answer 1

\[1000 \div(\pi(500/\pi ^{2/3})=2\sqrt[3]{500/\pi}\]

Answer 2

I think (500/pi) is raised to 2/3 and not just pi^(2/3) as you have shown above.

Answer 3

\(\Large \pi * (\frac {500}{\pi})^{2/3} = \pi * (500)^{2/3} * (\pi)^{-2/3} =
(500)^{2/3} * (\pi)^{1/3} = \\ \Large
\frac{500}{500^{1/3}} * (\pi)^{1/3} = 500 * \sqrt [3]{\frac {\pi}{500}} \\ \Large
1000 \div 500 * \sqrt [3]{\frac {\pi}{500}} = 2 * \sqrt [3]{\frac {\pi}{500}}

\)

Answer 4

In the last line I forgot to flip the fraction (due to division):

\( \Large
1000 \div (500 * \sqrt [3]{\frac {\pi}{500}}) = 2 * \sqrt [3]{\frac {500}{\pi}}
\)