Question

\(\frac{2\cdot5^{22}-9\cdot5^{21}}{25^{10}}:\frac{5\left(3\cdot7^{15}-19\cdot7^{\left(14\right)}\right)}{\left(7^{16}+3\cdot7^{15}\right)}\)

Answer 1

\(\dfrac{2.5^{22}-9.5^{21}}{25^{10}}:\dfrac{5\left(3.7^{15}-19.7^{\left(14\right)}\right)}{\left(7^{16}+3.7^{15}\right)}\)
\(=\dfrac{2.5^{20}.5^2-9.5^{20}.5}{25^{10}}:\dfrac{5\left[7^{14}\left(3.7-19\right)\right]}{7^{15}\left(7+3\right)}\)
\(=\dfrac{\left(5^2\right)^{10}\left(2.5^2-9.5\right)}{25^{10}}:\dfrac{5\left[7^{14}\left(21-19\right)\right]}{7^{15}.10}\)
\(=\dfrac{25^{10}\left(2.5^2-9.5\right)}{25^{10}}:\dfrac{5.7^{14}.2}{7^{15}.10}\)
\(=2.5^2-9.5:\dfrac{2}{7.2}\)
\(=5.\left(2.5-9\right):\dfrac{2}{14}\)
\(=5.\left(10-9\right):\dfrac{1}{7}\)
\(=5.1.7\)
\(=35\)