\(=\dfrac{\left(\dfrac{35721}{4}\right)\cdot2.5^6}{\left(-\dfrac{15}{4}\right)^5}=\dfrac{3^6\cdot7^2}{4}\cdot\dfrac{5^6}{2^6}:\dfrac{-3^5\cdot5^5}{2^{10}}\)

\(=\dfrac{3^6\cdot7^2\cdot5^6}{2^8}\cdot\dfrac{2^{10}}{-3^5\cdot5^5}=-2^2\cdot3\cdot5\cdot7^2=-2940\)

\(=\)\(\frac{2^{12}.5^7+2^{12}.5^6}{2^{15}.5^6+2^{12}.5^6}\)

\(=\)\(\frac{2^{12}.5^6.\left(1+5\right)}{2^{12}.5^6.\left(2^3+1\right)}\)

\(=\)\(\frac{6}{9}\)\(=\)\(\frac{2}{3}\)

chúc học tốt

0,5555897934

\(\frac{2^{12}\cdot5^7+4^6\cdot25^3}{8^5\cdot25^3+\left(2^2\cdot5\right)^6}\)

\(=\frac{2^{12}.5^7+2^{12}\cdot5^6}{2^{15}\cdot5^6+2^{12}\cdot5^6}\)

\(=\frac{2^{12}\cdot5^6\cdot\left(1\cdot5+1\right)}{2^{12}\cdot5^6\cdot\left(2^3\cdot1+1\right)}\)

\(=\frac{6}{9}\)

\(=\frac{2}{3}\)

\(=\dfrac{5^3\left(2^3+2+1\right)}{55}-\dfrac{2^{12}\cdot3^{10}+2^{12}\cdot3^{10}\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}\)

\(=5^2-\dfrac{2^{12}\cdot3^{10}\cdot\left(1+5\right)}{2^{11}\cdot3^{11}\left(2\cdot3-1\right)}=25-\dfrac{2}{3}\cdot\dfrac{6}{5}\)

=25-4/5

=24,2

Lời giải:

1.

$3^{x+2}+4.3^{x+1}=7.3^6$

$3^{x+1}.3+4.3^{x+1}=7.3^6$

$3^{x+1}(3+4)=7.3^6$

$3^{x+1}.7=7.3^6$

$\Rightarrow 3^{x+1}=3^6$

$\Rightarrow x+1=6$

$\Rightarrow x=5$

2.

$5^{x+4}-3.5^{x+3}=2.5^{11}$

$5^{x+3}.5-3.5^{x+3}=2.5^{11}$

$5^{x+3}(5-3)=2.5^{11}$

$2.5^{x+3}=2.5^{11}$

$\Rightarrow 5^{x+3}=5^{11}$

$\Rightarrow x+3=11$

$\Rightarrow x=8$

3.

$4^{x+3}-3.4^{x+1}=13.4^{11}$

$4^{x+1}.4^2-3.4^{x+1}=13.4^{11}$

$4^{x+1}.16-3.4^{x+1}=13.4^{11}$

$13.4^{x+1}=13.4^{11}$

$\Rightarrow 4^{x+1}=4^{11}$

$\Rightarrow x+1=11$
$\Rightarrow x=10$