Question

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

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Answer 1

\(A=\dfrac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^6\cdot3^3+2^{12}\cdot3^5}-\dfrac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+5^9\cdot7^3\cdot2^3}\)

\(=\dfrac{2^{12}\cdot3^4\cdot\left(3-1\right)}{2^6\cdot3^3\cdot\left(1+2^6\cdot3^2\right)}-\dfrac{5^{10}\cdot7^3\cdot\left(1-7\right)}{5^9\cdot7^3\cdot\left(1+2^3\right)}\)

\(=\dfrac{2^6\cdot3\cdot2}{1+64\cdot9}-\dfrac{5\cdot\left(-6\right)}{9}\)

\(=\dfrac{2^7\cdot3}{1+576}+\dfrac{30}{9}\)

\(=\dfrac{384}{577}+\dfrac{30}{9}=\dfrac{384}{577}+\dfrac{10}{3}=\dfrac{6922}{1731}\)