Question

Rút gọn : \(A=\frac{20^{15}.15^{12}}{25^{14}.6^{14}.8^5}\)

Answer 1

\(A=\frac{4^{15}.5^{15}.3^{12}.5^{12}}{5^{28}.2^{14}.3^{14}.2^{15}}=\frac{2.2^{29}.5^{27}.3^{12}}{5.5^{27}.2^{29}.3^{12}.3^2}=\frac{2}{45}\)

Answer 2

\(A=\frac{20^{15}.15^{12}}{25^{14}.6^{14}.8^5}=\frac{\left(2^2.5\right)^{15}.\left(3.5\right)^{12}}{\left(5^2\right)^{14}.\left(2.3\right)^{14}.\left(2^3\right)^5}=\frac{\left(2^2\right)^{15}.5^{15}.3^{12}.5^{12}}{5^{28}.2^{14}.3^{14}.2^{15}}\)

=\(\frac{2^{30}.3^{12}.5^{15}.5^{12}}{5^{28}.3^{14}.2^{14}.2^{15}}=\frac{2^{30}.3^{12}.5^{27}}{5^{28}.3^{14}.2^{29}}=\frac{2}{5.3^2}=\frac{2}{45}\)