\(\dfrac{2^7\cdot9^3}{6^5\cdot8^2}\)
\(=\dfrac{2^7\cdot\left(3^2\right)^3}{2^5\cdot3^5\cdot\left(2^3\right)^2}\)
\(=\dfrac{2^7\cdot3^6}{2^{11}\cdot3^5}\)
\(=\dfrac{1\cdot3}{2^4\cdot1}\)
\(=\dfrac{3}{16}\)
\(=\dfrac{2^7\cdot3^6}{2^5\cdot3^5\cdot2^6}=\dfrac{3}{2^4}=\dfrac{3}{16}\)
\(\dfrac{2^7\cdot9^3}{6^5\cdot8^2}=\dfrac{2^7\cdot\left(3^2\right)^3}{\left(2\cdot3\right)^5\cdot\left(2^3\right)^2}\\ =\dfrac{2^7\cdot3^6}{2^5\cdot3^5\cdot2^6}=\dfrac{2^7\cdot3}{2^{11}}\\ =\dfrac{3}{2^4}=\dfrac{3}{16}\)
