What are the dimensions of a&b in the relation F = at+bx, where f is force and x is distance?

What are the dimensions of a&b in the relation F = at+bx, where f is f

1.	What are the dimensions of a&b in the relation F = at+bx, where f is force and x is distance?
Answer» {tex}\\begin{array}{l}F\\;=\\;a+\\;bx\\\\Since\\;a\\;is\\;connected\\;by\\;addition\\;symbol\\;so\\;a\\;has\\;dimension\\;same\\;as\\;F\\\\\\lbrack F\\rbrack=\\;\\lbrack a\\rbrack\\;=\\;\\lbrack MLT^{-2}\\rbrack\\\\let\\;\\lbrack b\\rbrack\\;=\\;\\lbrack M^xL^yT^z\\rbrack\\\\Again\\;bx\\;has\\;dimension\\;of\\;F\\\\\\lbrack F\\rbrack\\;=\\;\\lbrack b\\rbrack\\lbrack x\\rbrack\\\\=\\;>\\;\\lbrack MLT^{-2}\\rbrack\\;=\\;\\lbrack M^xL^yT^z\\rbrack\\lbrack L\\rbrack\\\\=>\\;\\lbrack MLT^{-2}\\rbrack\\;=\\;\\lbrack M^xL^{y+1}T^z\\rbrack\\\\comparing\\;the\\;powers\\;of\\;M,L\\;and\\;T\\\\x=1\\\\y+1=1\\\\=>\\;y=0\\\\z=-2\\\\so\\;\\lbrack b\\rbrack\\;=\\;\\lbrack M^xL^yT^z\\rbrack=\\;\\lbrack M^1L^0T^{-2}\\rbrack\\;\\\\\\lbrack b\\rbrack=\\;\\lbrack M^1T^2\\rbrack\\end{array}{/tex}