1. Without using a pocket calculator, calculate the value of the expression $2^{3} \cdot 3^{-9} \cdot 6^{6} \cdot 8^{-8} \cdot 1728$. The result should be written in the form of a power.
1. The number $1728 \mathrm{v}$ in the expression $2^{3} \cdot 3^{-9} \cdot 6^{6} \cdot 8^{-8} \cdot 1728$ can be factored into prime factors as $1728=2^{6} \cdot 3^{3}$. We write $6^{6}=(2 \cdot 3)^{6}=2^{6} \cdot 3^{6}$ and $8^{-8}=2^{-24}$. We apply the rules for multiplying powers with the same base: we keep the base and add the exponents, resulting in $2^{-9}$.

![](https://cdn.mathpix.com/cropped/2024_06_07_59669f975316a35884bfg-06.jpg?height=257&width=1644&top_left_y=1431&top_left_x=203)