\(A=\dfrac{2^{15}.3^5-4^6.9^2}{\left(2^2.3\right)+8^4.3^5}-\dfrac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
\(\Leftrightarrow A=\dfrac{2^{15}.3^5-\left(2^2\right)^6.\left(3^2\right)^2}{2^2.3+\left(2^3\right)^4.3^5}-\dfrac{5^{10}.7^3-\left(5^2\right)^5.\left(7^2\right)^2}{\left(5^3\right)^3.7^3+5^9.14^3}\)
\(\Leftrightarrow A=\dfrac{2^{15}.3^5-2^{12}.3^4}{2^2.3+2^{12}.3^5}-\dfrac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.\left(7.2\right)^3}\)
\(\Leftrightarrow A=\dfrac{2^{12}.3^4\left(2^3.3-1\right)}{2^2.3\left(1+2^{10}.3^4\right)}-\dfrac{5^{10}.7^3\left(1-7\right)}{5^9.7^3\left(1+2^3\right)}\)
\(\Leftrightarrow A=\dfrac{2^{10}.3^3\left(2^3.3-1\right)}{\left(1+2^{10}.3^4\right)}-\dfrac{5\left(1-7\right)}{\left(1+2^3\right)}\)
\(\Leftrightarrow A=\dfrac{1024.9\left(8.3-1\right)}{\left(1+1024.81\right)}-\dfrac{5\left(1-7\right)}{\left(1+8\right)}\)
\(\Leftrightarrow A=\dfrac{9216\left(24-1\right)}{\left(1+82944\right)}-\dfrac{5\left(1-7\right)}{\left(1+8\right)}\)
\(\Leftrightarrow A=\dfrac{9216.23}{82945}-\dfrac{5\left(-6\right)}{9}\)
\(\Leftrightarrow A=\dfrac{211968}{82945}+\dfrac{30}{9}\)
\(\Leftrightarrow A=\dfrac{1907712}{746505}+\dfrac{2488350}{746505}\)
\(\Leftrightarrow A=\dfrac{1907712+2488350}{746505}\)
\(\Leftrightarrow A=\dfrac{4396062}{746505}\)
