Final answer:
If the two separate samples of red powder have identical elemental composition, they are likely the same compound, as per the law of definite proportions.
Step-by-step explanation:
The question asks whether two separate samples of a solid red powder can be the same compound and which law explains why.
The principle in question is the law of constant composition, also known as the law of definite proportions, which states that all samples of a pure compound contain the same elements in the same proportions by mass. Therefore, if the elemental composition of the two red powder samples is identical in proportion, the samples are likely the same compound. If the compositions differ, they are different compounds.