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I don't think it is required to memorize that Joules is also kg*m^2*s^-2. However, there are times when it would help to know these alternative units to figure out the answer. For example, for Debroglie's wavelength, to find the wavelength of an "object," you would need to know the mass and velocity of said object. The thing is, sometimes a problem may use another unit of mass or velocity (for mass: perhaps pounds, tons, or simply grams, rather than just kg; for velocity: perhaps mph rather than just m/s.) For our current chapter, in order to use equations with Planck's constant (in this case, the Debroglie wavelength formula), you would need to convert the mass into kg and the velocity into m/s, because the units for this constant is J*s, and Joules contains the units kg and m/s. Knowing that Joules is also kg*m^2*s^-2 will help you figure out what exactly you need in order to find a certain variable (and it will reassure you through dimensional analysis that you're using the right numbers and yielding the correct units for the answer). Not sure if there will be a problem in which energy will be written in these units, but, for the most part, no.
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