Question

\(\dfrac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}^{ }-\dfrac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)

Answer 1

\(\dfrac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\dfrac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)

\(=\dfrac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\dfrac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.7^3.2^3}\)

\(=\dfrac{2^{12}(3^5-3^4)}{2^{12}(3^6+3^5)}-\dfrac{5^{10}(7^3-7^4)}{5^9.7^3(1+2^3)}\)

\(=\dfrac{2^{12}.162}{2^{12}.972}-\dfrac{5^{10}(-2058)}{5^9.7^3.9}\)

\(=\dfrac{2^{12}.162}{2^{12}.972}-\dfrac{5^{10}(-2058)}{5^9.7^3.9}\)

\(=\dfrac{162}{972}-\dfrac{5(-2058)}{7^3.9}\)

\(=\dfrac{2.3^4}{2^2.3^5}-\dfrac{5.2.7^3.\left(-3\right)}{7^3.3^2}\)

\(=\dfrac{1}{2.3}-\left(\dfrac{-\left(5.2\right)}{3}\right)\)

\(=\dfrac{1}{6}-\left(\dfrac{-10}{3}\right)\)

\(=\dfrac{7}{2}\)