How did he get the fraction with fraction power?

So we have a simple equation that is from Kepler.

${\left(\frac{{\overline{r}}_{1}}{{\overline{r}}_{2}}\right)}^{3}={\left(\frac{{T}_{1}}{{T}_{2}}\right)}^{2}$

In an explanation of a physics book, you can resolve for ${r}_{2}$ like this:

${r}_{2}={r}_{1}{\left(\frac{{T}_{1}}{{T}_{2}}\right)}^{2/3}$

And I found

${r}_{1}=\sqrt[3]{\frac{{T}_{1}^{2}}{{T}_{2}^{2}}{r}_{2}^{3}}$

First question, is my approach correct? My second and main question is how did he get the ${r}_{2}$ equation that I stated first. The physics book doesn't explain how to get from the main equation to ${r}_{2}={r}_{1}{\left(\frac{{T}_{1}}{{T}_{2}}\right)}^{2/3}$. Can someone explain me, please? (By the way, of course the equation for ${r}_{1}$ and ${r}_{2}$ should be different).

Thank you!

So we have a simple equation that is from Kepler.

${\left(\frac{{\overline{r}}_{1}}{{\overline{r}}_{2}}\right)}^{3}={\left(\frac{{T}_{1}}{{T}_{2}}\right)}^{2}$

In an explanation of a physics book, you can resolve for ${r}_{2}$ like this:

${r}_{2}={r}_{1}{\left(\frac{{T}_{1}}{{T}_{2}}\right)}^{2/3}$

And I found

${r}_{1}=\sqrt[3]{\frac{{T}_{1}^{2}}{{T}_{2}^{2}}{r}_{2}^{3}}$

First question, is my approach correct? My second and main question is how did he get the ${r}_{2}$ equation that I stated first. The physics book doesn't explain how to get from the main equation to ${r}_{2}={r}_{1}{\left(\frac{{T}_{1}}{{T}_{2}}\right)}^{2/3}$. Can someone explain me, please? (By the way, of course the equation for ${r}_{1}$ and ${r}_{2}$ should be different).

Thank you!