[tex]\displaystyle\\
\left(\frac{1}{10}\right)^{15}\times\left(\frac{1}{1000}\right)^{-6}=\\\\\\
=\left(\frac{1}{10}\right)^{15}\times\left(\frac{1}{10^3}\right)^{-6}=\\\\\\
=\left(\frac{1}{10}\right)^{15}\times\left[\left(\frac{1}{10}\right)^3\right]^{-6}= \\\\\\
=\left(\frac{1}{10}\right)^{15}\times\left(\frac{1}{10} \right)^{3\times(-6)}=\\\\\\
=\left(\frac{1}{10}\right)^{15}\times\left(\frac{1}{10}\right)^{-18}=\\\\\\
=\left(\frac{1}{10}\right)^{15+(-18)}=\left(\frac{1}{10}\right)^{-3}=\boxed{10^3}
[/tex]
