Yes, if the process is occurring under an isothermal condition where change in T=0
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If you set a function equal to zero and solve for x, then you are finding where the function crosses the x-axis.
The question doesn't make sense, because any nonzero number raised to the zero (0) power (exponent) will always equal one (1).
370 = 1 ======any number to the power of zero will equal 1
The antiderivative of a function which is equal to 0 everywhere is a function equal to 0 everywhere.
Not sure what you mean by "zero element". If an expression is equal to zero, and you can factor it, then at least one of the factors must be zero; this is often useful to solve an equation.