a)
\(A=\dfrac{6^5-3^5.31}{12^5+3^5}\\ =\dfrac{2^5.3^5-3^5.31}{3^5.4^5+3^5}\\ =\dfrac{3^5\left(2^5-31\right)}{3^5\left(4^5+1\right)}\\ =\dfrac{2^5-31}{4^5+1}\\ =\dfrac{32-31}{1024+1}\\ =\dfrac{1}{1025}\)
\(A=\dfrac{6^5-3^5\cdot31}{12^5+3^5}\)
\(A=\dfrac{2^5\cdot3^5-3^5\cdot31}{\left(2^2\right)^5\cdot3^5+3^5}\)
\(A=\dfrac{3^5\cdot\left(2^5-31\right)}{3^5\cdot\left(2^{10}+1\right)}\)
\(A=\dfrac{32-31}{1024+1}\)
\(A=\dfrac{1}{1025}\)
\(a,A=\dfrac{6^5-3^5.31}{12^5+3^5}=\dfrac{\left(3.2\right)^5-3^5.31}{\left(3.2^2\right)^5+3^5}\)
\(=\dfrac{3^5.2^5-3^5.31}{3^5.2^{10}+3^5}\)\(=\dfrac{3^5\left(2^5-31\right)}{3^5\left(2^{10}+1\right)}\)
\(=\dfrac{1}{1025}\)
\(a,A=\dfrac{6^5-3^5.31}{12^5+3^5}=\dfrac{\left(3.2\right)^5-3^5.31}{\left(3.2^2\right)^5+3^5}\)
\(=\dfrac{3^5.2^5-3^5.31}{3^5.2^{10}+3^5}\)\(=\dfrac{3^5\left(2^5-31\right)}{3^5\left(2^{10}+1\right)}\)
\(=\dfrac{1}{1025}\)