các bạn giúp mình giải đáp nhé ạ 🙂

Bài $2:$

$a)$ $5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9$

$4^{15}=2^{30},\quad9^9=3^{18},\quad8^9=2^{27}$

$=5\cdot2^{30}\cdot3^{18}-4\cdot3^{20}\cdot2^{27}$

$=2^{27}\cdot3^{18}(5\cdot2^3-4\cdot3^2)=2^{27}\cdot3^{18}\cdot4$

$=2^{29}\cdot3^{18}$

Mẫu số:

$5\cdot2^{29}\cdot9^{16}-7\cdot2^{29}\cdot27^6$

$=2^{29}(5\cdot3^{32}-7\cdot3^{36})=2^{29}\cdot3^{32}(5-7\cdot3^4)$

$=-562\cdot2^{29}\cdot3^{32}$

$\Rightarrow\dfrac{2^{29}\cdot3^{18}}{-562\cdot2^{29}\cdot3^{32}}=-\dfrac{1}{562\cdot3^{14}}$

$b)$ $\dfrac{2^4\cdot5^2\cdot14^2\cdot7}{2^3\cdot5^3\cdot7^2\cdot14}$

$14=2\cdot7\Rightarrow14^2=2^2\cdot7^2$

$=\dfrac{2^6\cdot5^2\cdot7^3}{2^4\cdot5^3\cdot7^3}$

$=\dfrac{2^2}{5}$

$=\dfrac{4}{5}$

$c)$ $\dfrac{5^{14}\cdot7^{12}+5^{14}\cdot7^{11}}{5^{12}\cdot7^{11}+9\cdot5^{14}\cdot7^{11}}$

$=\dfrac{5^{14}\cdot7^{11}(7+1)}{5^{12}\cdot7^{11}(1+9\cdot5^2)}$

$=\dfrac{8\cdot5^{14}}{226\cdot5^{12}}=\dfrac{8\cdot25}{226}$

$=\dfrac{100}{113}$