$\frac{{64}^{-5}\cdot {\left(\sqrt[4]{256}\right)}^{-3}}{\sqrt[3]{4^{15}}}=\frac{{\left(2^6\right)}^{-5}\cdot {\left(\sqrt[4]{4^4}\right)}^{-3}}{{\left(4^{15}\right)}^{\frac{1}{3}}}=$  

$=\frac{2^{6\cdot \left(-5\right)}\cdot 4^{-3}}{4^{15\cdot \frac{1}{3}}}=\frac{2^{-30}\cdot {\left(2^2\right)}^{-3}}{4^5}=$     

$=\frac{2^{-30}\cdot 2^{2\cdot \left(-3\right)}}{{\left(2^2\right)}^5}=\frac{2^{-30}\cdot 2^{-6}}{2^{2\cdot 5}}=$  

$=\frac{2^{-30-6}}{2^{10}}=2^{-36-10}=2^{-46}$