To find the volume of the rectangular prism made up of 4 cubes that are each 15 inches on a side, we first calculate the volume of one cube:
\[ \text{Volume of one cube} = \text{side}^3 = 15^3 = 15 \times 15 \times 15 = 3375 \text{ cubic inches}. \]
Since there are 4 cubes, the total volume \( V \) is:
\[ V = 4 \times 3375 = 13500 \text{ cubic inches}. \]
Now, we can simplify this to a fraction in lowest terms.
The total volume, 13500 cubic inches, can be expressed as a fraction over 1:
\[ 13500 = \frac{13500}{1}. \]
Now, let's see which option matches a sensible probability for the dimensions given originally in the question (which might hint at a need to adjust for scale). However, the options given are small fractions.
Since none of the options seem to relate directly to our calculated volume of 13500 cubic inches, let's analyze them with respect to potential reductions:
- \( \frac{4}{25} \) cubic inches
- \( \frac{4}{5} \) cubic inches
- \( \frac{4}{125} \) cubic inches
- \( 1 \) cubic inch
To find out if these could represent parts of something larger:
13500 divided by any of these fractions should yield a whole number multiple of the cube dimension scale. However, if we calculate for simplification, none correspond directly.
After doing calculations again, since none of the unit fractions or cubic calculations reduce correctly, it seems possible the values don’t apply.
In conclusion, if you're asking for the closest volumetric representation or adjustment to parameters provided in the volumetric question the answer remains unmatched. Thus, it might be useful to note that the simplistic fractions don’t line up with dimensional outputs directly or relatively, however:
If forced to assimilate an answer, the simplest smaller fraction representation nearest in volumetric perspective regards a 1 inch cubic representing a small transfer scaling element: (1 cubic inch) could be regarded as a final answer.
But still keep in context the total from above suggests 13500 cubic inches, thus needing clarification against options as none are truly representative.
I recommend seeking out clarification or further scaling of values based on initial illustration or dimensional charts if applicable.