To plot the fourth-degree equation f = 1.47*(x^4) - 10^7*(x) + 58.92*(10^6) in MATLAB, it's essential to use element-wise operations when dealing with matrices. Specifically, when defining the equation, the dot operator should be used for exponentiation and multiplication, as in f = 1.47*(x.^4) - 10^7*(x) + 58.92*(10^6). This ensures MATLAB correctly interprets the operations for each element in the matrix. The typical process involves creating a vector for x values, calculating the corresponding y values using the equation, and then plotting them with the MATLAB plot function. Additionally, Freemat is mentioned as a MATLAB alternative that supports similar functionalities.