\(c,A=\dfrac{2^7\cdot6^5-36^2\cdot4^4}{128\cdot6^5+2^{12}\cdot243}\)
\(=\dfrac{2^7\cdot\left(2\cdot3\right)^5-\left(2^2\cdot3^2\right)^2\cdot\left(2^2\right)^4}{2^7\cdot\left(2\cdot3\right)^5+2^{12}\cdot3^5}\)
\(=\dfrac{2^7\cdot2^5\cdot3^5-2^4\cdot3^4\cdot2^8}{2^7\cdot2^5\cdot3^5+2^{12}\cdot3^5}\)
\(=\dfrac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{12}\cdot3^5+2^{12}\cdot3^5}\)
\(=\dfrac{2^{12}\cdot3^4\cdot\left(3-1\right)}{2\cdot\left(2^{12}\cdot3^5\right)}\)
\(=\dfrac{2^{12}\cdot3^4\cdot2}{2\cdot2^{12}\cdot3^5}\)
\(=\dfrac{1}{3}\)
\(---\)
\(d,\dfrac{5^7\cdot35^3+25^5\cdot49^2}{\left(125\cdot7\right)^3\cdot2+5^9\cdot14^3}\)
\(=\dfrac{5^7\cdot\left(5\cdot7\right)^3+\left(5^2\right)^5\cdot\left(7^2\right)^2}{125^3\cdot7^3\cdot2+5^9\cdot\left(2\cdot7\right)^3}\)
\(=\dfrac{5^7\cdot5^3\cdot7^3+5^{10}\cdot7^4}{\left(5^3\right)^3\cdot7^3\cdot2+5^9\cdot2^3\cdot7^3}\)
\(=\dfrac{5^{10}\cdot7^3+5^{10}\cdot7^4}{5^9\cdot7^3\cdot2+5^9\cdot7^3\cdot8}\)
\(=\dfrac{5^{10}\cdot7^3\cdot\left(1+7\right)}{5^9\cdot7^3\cdot\left(2+8\right)}\)
\(=\dfrac{5\cdot8}{10}\)
\(=\dfrac{40}{10}=4\)
#\(Toru\)
