[tex]\begin{aligned}\left[\left(5^4\right)^5\right]^3 :\left(5\cdot 5^{15}\right)^3 &= \left(5^{4\cdot 5}\right)^3 : \left(5^{1+15}\right)^3\\ &= \left(5^{20}\right)^{3}:\left(5^{16}\right)^3\\ &= 5^{20\cdot 3} :5^{16\cdot 3} \\ &= 5^{60}:5^{48} \\ &= 5^{60-48} \\ &= 5^{12}\end{aligned}[/tex]
