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First, we need to convert all the measurements to improper fractions:
Length = 10 2/5 in. = 52/5 in.
Width = 8 1/2 in. = 17/2 in.
Height = 6 1/4 in. = 25/4 in.
Now, we can plug these values into the formula:
V = (52/5)(17/2)(25/4)
V = (52*17*25) / (5*2*4)
V = 22100 / 40
V = 552.5
Therefore, the volume of the rectangular prism is 552 1/2 cubic inches or 552.5 cubic inches.