Simplify $\dfrac{5^4 \cdot 8 \cdot 16}{2^7 \cdot 125}$ (Example 2):

Express everything in primes: $5^4\cdot 2^3\cdot 2^4=5^4\cdot 2^7$ over $2^7\cdot 5^3$, so the $2^7$ cancels and $5^4/5^3=5^{1}=5$. The simplified value is $5$.