Сравните числа: 1)3^3^3 и 3^33 2)2^22 и 2^2^2 Вычислите: 1)10^4 * 10^4/25^4 2)(3/7)^3 *...

1) $3^{3^3}=3^{27}\ \textless \ 3^{33}$
2) $2^{22}\ \textless \ 2^{2^2}=2^4$

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1) $10^4 * \frac{10^4}{25^4}= 10^4 * (\frac{10}{25})^4= (10* \frac{10}{25} )^4= (\frac{100}{25}) ^4=( \frac{25*4}{25*1} )^4= (\frac{4}{1} )^4=$
$=4^4=4^{2*2}=(4^2)^2=(16)^2=16^2=256$

2) $( \frac{3}{7} )^3* (\frac{7}{9} )^3=( \frac{3}{7}* \frac{7}{9} )^3= (\frac{3*7*1}{3*7*3})^3 = (\frac{1}{3}) ^3= \frac{1^3}{3^3}= \frac{1}{27}$

3) $0.25^{10} * 4^{10}=(0.25*4)^{10}=(1)^{10}=1$

4) $81 * \frac{27^4}{3^9}= \frac{81*27^4}{3^9}= \frac{9^2*(3^3)^4}{3^9}= \frac{(3^2)^2*3^{3*4}}{3^9}= \frac{3^{2*2}*3^{12}}{3^9}= \frac{3^4*3^{12}}{3^9}= \frac{3^{4+12}}{3^9} =$
$= \frac{3^{4+12}}{3^9} =\frac{3^{16}}{3^9} = \frac{3^{9+7}}{3^9}= \frac{3^9*3^7}{3^9*1} =\frac{3^7}{1} =3^7=(3^3)^2*3^1=(27)^2*3=$
$=729*3=2187$