Final answer:
The student is attempting a conversion that involves squared units, such as cm² to m². To do this accurately, the conversion factor for the base unit centimeter to meter, which is 10⁻², must be squared, resulting in 10⁻⁴ for squared units. Without an exact equation, the answer is not definitive, but option (b) 2 is suggested based on dimensional analysis.
Step-by-step explanation:
The student needs to determine the conversion factor to fill in the missing part of the equation. Considering the example provided for area conversion, where 1 cm² equals 10⁻⁴ m², we can understand that when converting units of measure in squared units (such as from cm² to m²), we need to square the conversion factor between the base units.
For the equation X10x10cm⁻².0기X5 ?, although there are typos, it seems to represent a unit conversion that is not entirely clear because of the errors in the equation. However, taking a similar approach to the provided examples, we calculate by raising the conversion factor for individual units to the power that matches the square in cm². For example, converting from centimeters to meters involves dividing by 100 for the base unit. Hence, converting cm² to m² would involve dividing by 100², which is 10,000, representing a conversion factor of 10⁻⁴ when squared.
If we look at the options provided and consider the dimensional analysis for square units, we can say that the correct answer is likely option (b) 2 when considering proper unit conversions. Without a clearer context or correctly stated equation, we can't provide an exact answer, but we can guide the thought process based on what we know about unit conversions.