$\text{I.}$

$2^{-3}\cdot 2^5\cdot 2^3=2^{\left(-3\right)+5+3}=2^5$

 

$\text{II.}$

${\left(-4\right)}^{-5}\cdot {\left(-4\right)}^4\cdot {\left(-4\right)}^{-2}={\left(-4\right)}^{\left(-5\right)+4+\left(-2\right)}={\left(-4\right)}^{-3}={\left({\left(-\frac{1}{4}\right)}^{-1}\right)}^{-3}={\left(-\frac{1}{4}\right)}^3=-\frac{1}{64}$

 

$\text{III.}$

${\left(\frac{5}{6}\right)}^{10}\cdot {\left(\frac{5}{6}\right)}^{-15}\cdot {\left(\frac{5}{6}\right)}^3={\left(\frac{5}{6}\right)}^{10+\left(-15\right)+3}={\left(\frac{5}{6}\right)}^{-2}={\left(\frac{6}{5}\right)}^2=\frac{6^2}{5^2}=$

$=\frac{36}{25}=1\frac{11}{25}=1\frac{44}{100}=1,44$

 

$\text{IV.}$

${0,4}^{-8}\cdot {0,4}^6\cdot {0,4}^4\cdot {0,4}^{-5}={0,4}^{\left(-8\right)+6+4+\left(-5\right)}={\left(\frac{4}{10}\right)}^{-3}={\left(\frac{10}{4}\right)}^3=\frac{1000}{64}=15\frac{40}{64}=15\frac{5}{8}$