For the equation F=A^ a ^ b ^ c , where F is the force, A is the...

\left[\mathrm{MLT}^{-2}\right]=\left[$\mathrm{L}^{2 \mathrm{a}}$\right]\times\left[$\mathrm{L}^{\mathrm{b}}$ \mathrm{T}^{-\mathrm{b} }\right] \left[$\mathrm{M}^{\mathrm{c}}$ \mathrm{L}^{-3 \mathrm{c} }\right]=\left[\mathrm{M}^{$$\mathrm{c}$$} \mathrm{L}^{2 \mathrm{a}+\mathrm{b}-$3 $\mathrm{c}$} $\mathrm{T}^{-\mathrm{b}}\right]$ Comparing powers of $\mathrm{M}$, $\mathrm{L}$ and $\mathrm{T}$, on both sides, we get\begin{array}{l} \mathrm{c}=1,2 \mathrm{a}+\mathrm{b}-3 \mathrm{c}=1,- \mathrm{b}=-2 \text{ or } \mathrm{b}=2 \\ \text{ Also, }2 \mathrm{a}+2-3(1)=1 \Rightarrow 2 \mathrm{a}=2 \text{ or } \mathrm{a}=1 \end{array}$$\therefore$ This is 1,2,1