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a. 2\(\left(2^{-1}+3^{-1}\right):\left(2^{-1}-3^{-1}\right)+\left(2^{-1}:2^0\right):2^3\)
= \(\left(\frac12+\frac13\right):\left(\frac12-\frac13\right)+\left(\frac12:1\right):8\)
=\(\left(\frac36+\frac26\right):\left(\frac36-\frac26\right)+\left(\frac12\right):8\)
= \(\left(\frac56:\frac16\right)+\left(\frac{1}{2_{}}\right):8\)
= \(5+\frac12:8\)
= \(5+\frac{1}{16}\)
= \(\frac51+\frac{1}{16}=\frac{80}{16}+\frac{1}{16}=\frac{81}{16}\)
\(A=\dfrac{3^6\cdot3^8\cdot5^4-5^{13-9}\cdot3^{13}}{3^{12}\cdot5^6+3^{12}\cdot5^6}\)
\(=\dfrac{3^{14}\cdot5^4-5^4\cdot3^{13}}{3^{12}\cdot5^6\cdot2}\)
\(=\dfrac{3^{13}\cdot5^4\cdot2}{3^{12}\cdot5^6\cdot2}=\dfrac{3}{25}\)
\(B=\left(\dfrac{2}{5}\cdot5\right)^7+\left(\dfrac{9}{4}:\dfrac{3}{16}\right)^3=1+12^3=1729\)
\(=\left(\dfrac{2}{7}\cdot5\right)^7+\left(\dfrac{9}{4}:\dfrac{3}{16}\right)^3\)
\(=\left(\dfrac{10}{7}\right)^7+12^3\)