Descomponer y simplificar

\(\bullet\dfrac {2^{7}\cdot 2^{10}} {2^{8}\cdot 2^{5}=}\dfrac {2^{10+7}} {2^{8+5}}=2^{17-13}=\boxed{2^{4}}\)

\(\bullet\dfrac {18^{2}\cdot 150} {3^{3}\cdot 5^{2}}=\dfrac {\left( 2\cdot 3^{2}\right) ^{2}\cdot 2\cdot 3\cdot 5^{2}} {3^{3}\cdot 5^{2}}=\dfrac {2^{2}\cdot 3^{4}\cdot 2\cdot 3} {3^{3}}=2^{2+1}\cdot 3^{4+1-3}=\boxed{2^{3}\cdot 3^{2}}\)

\(\bullet\left[ \left( -2\right) ^{6}:\left( -2\right) ^{3}\right] ^{3}\cdot \left( -2\right) ^{0}\cdot \left( -2\right) ^{-4}=\left( \left( -2\right) ^{3}\right) ^{3}.\left( -2\right) ^{0}\cdot \left( -2\right) ^{-4}=\\

=\left( -2\right) ^{9}\cdot 1\cdot \left( -2\right) ^{-4}=\boxed{-2^{5}}\)

\(\bullet\dfrac {2^{10}\cdot 3^{4}\cdot 5^{6}} {65\cdot 10^{4}}=\dfrac {2^{10}\cdot 3^{4}\cdot 5^{6}} {\left( 2\cdot 3\right) ^{5}\cdot \left( 25\right) ^{4}}=\dfrac {2^{10}\cdot 3^{4}\cdot 5^{6}} {2^{5}\cdot 3^{5}\cdot 2^{4}\cdot 5^{4}}=\dfrac {2^{10}\cdot 3^{4}\cdot 5^{6}} {2^{9}\cdot 3^{5}\cdot 5^{4}}=\boxed{\dfrac {2\cdot 5^{2}} {3}}\)

\(\bullet\dfrac {36\cdot 25} {4\cdot 81}=\dfrac {{\not2^{2}}\cdot 3^{2}\cdot 5^{2}} {{\not2^{2}}\cdot 3^{4}}=\boxed{\dfrac {5^{2}} {3^{2}}}\)