Question

Найдите Значение Выражения
$5^{6} * ( frac{2}{5} )^{6}$
$4^{-3} * ( frac{3}{4} )^{-3}$
$( frac{2}{6} )^{5}$
$frac{8^{4} }{12^{3} }$
$frac{3^{-5} }{9^{-3} }$
$frac{10^{-5} }{15^{-3} }$

Answer 1

$5^6*( frac{2}{5})^6 = frac{5^6*2^6}{5^6} =2^6=64$

$4^{-3}*( frac{3}{4})^{-3} = frac{4^{-3}*3^{-3}}{4^{-3}} = 3^{-3}= frac{1}{27}$

$( frac{2}{6})^5 = frac{2^5}{(2*3)^5} =frac{2^5}{2^5*3^5}= frac{1}{3^5} = frac{1}{243}$

$frac{8^4}{12^3}= frac{2^{12}}{2^6*3^3}= frac{2^6}{3^3}= frac{64}{27}=2 frac{10}{27}$

$frac{3^{-5}}{9^{-3}}= frac{3^{-5}}{3^{-6}}=3$
 
$frac{10^{-5}}{15^{-3}}= frac{2^{-5}*5^{-5}}{3^{-3}*5^{-3}}= frac{3^3}{2^5*5^2}= frac{27}{32*25}= frac{27}{800}$

Answer 2

=$5^{6}* 2^{6} / 5^{6} = 2^{6} = 64$
=$4^{-3}* (3/4)^{-3} = (1/4)^{3} * (4/3)^{3} = (1/3)^{3} = 1/27$
=$(2/6)^{5} = (2/2*3)^{5} = (1/3)^{5} = 1/243$
= $8^{4} / 12^{3} = 2^{4}* 4^{4} / 3^{3} 4^{3} = 2^{4} 2^{2} / 3^{3}= 2^{6}/ 3^{3} =32/27$
= $3^{-5}/ 9^{-3} = 3^{-5} / 3^{-6} = 3$
= $10^{-5} / 15^{-3} = 2^{-5} 5^{-5} / 3^{-3} 5^{-3} = 3^{3} / 2^{5} 5^{2} = 27 / 800$