That's a misleading proof though.
 You mean this: \((\frac{a^{10}}{3})(\frac{b^7}{3})\)
 But I mean this: \((a^{\frac{10}{3}})(b^{\frac{7}{3}})\)
 There are major differences between the 2 equations.
 And I guess the asker means my equation because he said simplified radical form and that's a term for 'Law of Indices'.