What is the most efficient way to calculate the product ABC if
their dimensions are 10X5, 5X50, and 50X8, respectively?
I assume you mean calculate $\displaystyle 10\cdot5\cdot50\cdot5\cdot50\cdot50\cdot8$? Merely note that this is the same as $\displaystyle 5\cdot2\cdot5\cdot5\cdot5\cdot5\cdot2\cdot5\cdot5\ cdot5\cdot2\cdot2\cdot2\cdot2=5^9\cdot2^6$