Question

Thực hiện phép tính;

a)\(\frac{2.5^{22}-9.5^{21}}{25^{10}}\)

b) \(\frac{5.\left(3.7^{15}-19.7^{14}\right)}{7^{16}+3.7^{15}}\)

Answer 1

\(\frac{5\left(3.7^{15}-19.7^{14}\right)}{7^{16}+3.7^{15}}=\frac{5.\left[7^{14}\left(3.7-19\right)\right]}{7^{15}\left(7+3\right)}=\frac{5.7^{14}.2}{7^{15}.10}=\frac{2}{7.2}=\frac{2}{14}=\frac{1}{7}\)

Answer 2

a) \(\frac{2.5^{22}-9.5^{21}}{25^{10}}=\frac{5^{21}.\left(2.5-9\right)}{\left(5^2\right)^{10}}=\frac{5^{21}.1}{5^{20}}=5\)

b) \(\frac{5.\left(3.7^{15}-19.7^{14}\right)}{7^{16}+3.7^{15}}=\frac{5.7^{14}.\left(3.7-19\right)}{7^{15}.\left(7+3\right)}=\frac{5.7^{14}.2}{7^{15}.10}=\frac{1}{7}\)

Answer 3

a) \(\frac{2.5^{22}-9.5^{21}}{25^{10}}=\frac{2.5^{20}.5^2-9.5^{20}.5}{25^{10}}=\frac{\left(5^2\right)^{10}\left(2.5^2-9.5\right)}{25^{10}}=\frac{25^{10}\left(2.5^2-9.5\right)}{25^{10}}=2.5^2-9.5=5\left(2.5-9\right)=5.\left(10-9\right)=5.1=5\)