Какими формулами мы пользуемся?$$

$\log_ab = x \Leftrightarrow a^x = b$ 

$\displaystyle {a^{\log_ab} = b}$ 

$\displaystyle {\log _{a}b={\frac {\log _{c}b}{\log _{c}a}} }$

 ${\log _{a^{q}}{b}}^{p}={\frac {p}{q}}\log _{a}{b}$ 

$a^{\log_c b} = b^{\log_c a}$

$$
\displaystyle  { \sqrt [n] a = a^{ \frac {1} {n} }; (a^n)^m = a^{n \cdot m} }

$2^{3-7\sqrt {2}} \cdot 8^{7\sqrt {2} \over 3} = 2^{3-7\sqrt {2}} \cdot 2^{2^{7\sqrt {2} \over 3}} = 2^{3-7\sqrt {2}} \cdot 2^{2 \cdot{7\sqrt {2} \over 3}}$$\displaystyle { a^n \cdot a^m = a^{a+m} }$

$\displaystyle{ { \frac{a^x}{a^y}} = a^{x-y} }$ 

$3^{2+\log_9 16}= 3^2 *3^{\log_9 16}$

${\log_9 16} = {\log_{9} 2^4} = 4 \log_9 2$

$\displaystyle { 3^2 *3^{\log_9 16} = 9 *3^{4\log_9 2} = 9* 81^{\log_9 2} }$

$9*81^{\log_9 2} = 9*2^{\log_9 81} = 9*2^2=9*4 = 36$