question_answer

If \[\frac{{{5}^{m}}\times {{5}^{3}}\times {{5}^{-2}}}{{{5}^{-5}}}={{5}^{12}},\] find m.

Answer:

\[\frac{{{5}^{m}}\times {{5}^{3}}\times {{5}^{-2}}}{{{5}^{-5}}}={{5}^{12}}\]

\[{{5}^{m}}\times {{5}^{3}}\times {{5}^{-2}}\times {{5}^{5}}={{5}^{12}}\]

\[{{5}^{m}}\times {{5}^{3-2+5}}={{5}^{12}}\]

\[{{5}^{m}}\times {{5}^{6}}={{5}^{12}}\]

m+6=12

\[m=12-6\]

M=6