(13 supra8)^6 ÷(39supra32)^6=

(13/8)^6 : (39/32)^6 = 13^6/(2^3)^6 : (3x13)^6/(2^5)^6 = 13^6/2^18 : 3^6x13^6/2^30 = 13^6/2^18 x 2^30/3^6x13^6 = 2^12/3^6 = (2^2)^6/3^6 = 4^6/3^6 = (4/3)^6 

[tex] (\frac{13}{8})^{6} :(\frac{39}{32})^{6} = (\frac{13}{8})^{6}\cdot(\frac{32}{39})^{6}\\ \\ \frac{13^{6}}{8^{6}} \cdot \frac{32^{6}}{39^{6}}= \\ \\ \frac{13^{6}}{8^{6}} \cdot \frac{(8\cdot4)^{6}}{(3\cdot13)^{6}}= [/tex]

[tex] \frac{13^{6}}{8^{6}} \cdot \frac{8^{6}\cdot4^{6}}{3^{6}\cdot13^{6}}=(\frac{4}{3}) ^{6} [/tex]