Algebra Part 1

Starting with Jason's second expression here:


$$\frac{J}{J_{ref}}={\left(\frac{L}{L_{ref}}\right)}^{1/\mathrm{\kappa <!--\; \kappa \; -->}}$$


Raise both sides to the (κ - 1)th power:


$${\left(\frac{J}{J_{ref}}\right) }^{\mathrm{(}\mathrm{\kappa -1)<!--\; \kappa \; -->}}={\left(\frac{L}{L_{ref}}\right) }^{\mathrm{(}\mathrm{1-1/\kappa )<!--\; \kappa \; -->}}$$


Now divide both sides by the right side:


$${\left(\frac{J}{J_{ref}}\right)}^{\mathrm{\kappa <!--\; \kappa \; -->}-<!--\; -\; -->1}{\left(\frac{L}{L_{ref}}\right)}^{\mathrm{}<!--\; -\; -->1/\mathrm{\kappa \; -\; 1<!--\; \kappa \; -->}}=1$$