\(\dfrac{45^3\cdot14\cdot125}{180^5}\)
\(=\dfrac{\left(3^2\cdot5\right)^3\cdot2\cdot7\cdot5^3}{\left(2^2\cdot3^2\cdot5\right)^5}\)
\(=\dfrac{\left(3^2\right)^3\cdot5^3\cdot5^3\cdot2\cdot7}{\left(2^2\right)^5\cdot\left(3^2\right)^5\cdot5^5}\)
\(=\dfrac{3^6\cdot5^6\cdot2\cdot7}{2^{10}\cdot3^{10}\cdot5^5}\)
\(=\dfrac{7}{2^9\cdot3^4}\)
\(=\dfrac{7}{41472}\)
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