Answer:
\[{{n}_{2}}={{n}_{1}}{{\left[
\frac{{{M}_{1}}}{{{M}_{2}}} \right]}^{a}}{{\left[ \frac{{{L}_{1}}}{{{L}_{2}}}
\right]}^{b}}{{\left[ \frac{{{T}_{1}}}{{{T}_{2}}} \right]}^{c}}\]
\[=5{{\left[ \frac{1\,kg}{\alpha \,kg}
\right]}^{1}}{{\left[ \frac{1\,m}{\beta \,m} \right]}^{2}}{{\left[
\frac{1\,s}{\gamma \,s} \right]}^{-2}}\]
[as dimensional formula for energy is \[[{{M}^{1}}{{L}^{2}}{{T}^{-2}}]\]]
\[=5\left[ \frac{1}{\alpha } \right]\,{{\left[
\frac{1}{\beta } \right]}^{2}}{{\left[ \frac{1}{\gamma }
\right]}^{-2}}=\frac{5{{\gamma }^{2}}}{\alpha {{\beta }^{2}}}\]
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