question_answer

Simplify : \[\frac{{{(-2)}^{3}}\times {{(-2)}^{7}}}{3\times {{4}^{6}}}\]

Answer:

\[\frac{{{(-2)}^{3}}\times {{(-2)}^{7}}}{3\times {{4}^{6}}}=\frac{{{(-2)}^{3+7}}}{3\times {{({{2}^{2}})}^{6}}}\]

\[=\frac{{{(-2)}^{10}}}{3\times {{(2)}^{12}}}\]

\[=\frac{{{(-1)}^{10}}{{(2)}^{10}}}{3\times {{(2)}^{12}}}\]

\[=\frac{1\times {{(2)}^{10-12}}}{3}\]

\[=\frac{{{2}^{-2}}}{3}\]

\[=\frac{1}{3\times {{2}^{2}}}\]

\[=\frac{1}{12}\]