Final answer:
Paris incorrectly simplified the expression 10^3 · 10^{-1} as 100^{-2}. The correct simplification by adding the exponents would result in 10^2, which equals 100, not 1/10000 as implied by 100^{-2}.
Step-by-step explanation:
The question pertains to the simplification of an expression using the laws of exponents within the metric system. The expression given by the student, Paris, is 10^3 · 10^{-1}, which is intended to be simplified. The metric system simplifies such calculations by using powers of 10 for all conversions. When working with powers of 10, to multiply numbers like these, one should multiply any coefficients (the numbers in front of the powers) and then add the exponents. In the given expression, there are no coefficients other than 1, so we only have to deal with the exponents.
To correctly simplify the expression, we add the exponents: 3 + (-1) = 2. Therefore, the expression 10^3 · 10^{-1} simplifies to 10^2, which is equal to 100. It is clear that the student's simplification to 100^{-2} is incorrect, as 100^{-2} is equal to 1/10000 or 0.0001.
Understanding the powers of ten is essential, as our counting system is based on increases of ten due to historical reasons, such as humans originally counting with ten fingers. A strong grasp of these concepts helps not only in simplifying expressions but also in understanding the universal validity of mathematical rules, regardless of the context or application.