Let's use the following properties:
[tex]\begin{gathered} a^{-x}=\frac{1}{a^x} \\ x^y\cdot x^z=x^{y+z} \end{gathered}[/tex]Rewrite the expression as:
[tex]2^8\cdot2^{-5}\cdot5^9\cdot5^{-8}\cdot10^4\cdot10^{-7}=2^3\cdot5^1\cdot10^{-3}=\frac{1}{25}[/tex]