Ta có: \(12^{10}\cdot35+2^{10}\cdot65+6^2\cdot12^6\cdot15^2\)
\(=2^{20}\cdot3^{10}\cdot5\cdot7+2^{10}\cdot5\cdot13+2^2\cdot3^2\cdot2^{12}\cdot3^6\cdot3^2\cdot5^2\)
\(=2^{20}\cdot3^{10}\cdot5\cdot7+2^{10}\cdot5\cdot13+2^{14}\cdot3^{10}\cdot5^2\)
\(=2^{10}\cdot5\left(3^{10}\cdot7+13+2^4\cdot5\right)\)
Ta có: \(\frac{12^{10}\cdot35+2^{10}\cdot65+6^2\cdot12^6\cdot15^2}{2^8\cdot10^4}\)
\(=\frac{2^{10}\cdot5\left(3^{10}\cdot7+13+2^4\cdot5\right)}{2^8\cdot2^4\cdot5^4}=\frac{2^{10}\cdot5\cdot413436}{2^{12}\cdot5^4}=\frac{413436}{2^2\cdot5^3}=\frac{413436}{500}=\frac{103359}{125}\)
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