Problem 4. Calculate: $\frac{2^{3} \cdot 4^{5} \cdot 6^{7}}{8^{9} \cdot 10^{11}}: 0.015^{7}$.
Solution. We have:

$$
\begin{aligned}
\frac{2^{3} \cdot 4^{5} \cdot 6^{7}}{8^{9} \cdot 10^{11}}: 0.015^{7} & =\frac{2^{3} \cdot\left(2^{2}\right)^{5} \cdot 6^{7}}{\left(2^{3}\right)^{9} \cdot 10^{11}}:\left(\frac{15}{1000}\right)^{7}=\frac{2^{13}}{2^{27} \cdot 10^{11}} \cdot\left(\frac{6 \cdot 1000}{3 \cdot 5}\right)^{7} \\
& =\frac{1}{2^{14} \cdot 10^{11}} \cdot 400^{7}=\frac{1}{2^{14} \cdot 10^{11}} \cdot 4^{7} \cdot 100^{7} \\
& =\frac{1}{2^{14} \cdot 10^{11}} \cdot 2^{14} \cdot 10^{14}=10^{3}=1000
\end{aligned}
$$

## IX Department