Question

$8^{ frac{1}{4} +3 log^} 16^{32}$
$frac{ 20^{ log_{2}5 } }{ 10^{ log_{2} }5 }$

Answer 1

$1); 8^{frac{1}{4}+3log_{16}32}=8^{frac{1}{4}}cdot 8^{3log_{16}32}=A\\a); 3log_{16}32=3log_{16}(16cdot 2)=3(log_{16}16+log_{16}2)=\\=3(1+log_{2^4}2)=3(1+frac{1}{4}}log_22)=3(1+frac{1}{4})=3cdot frac{5}{4}=frac{15}{4}\\A=8^{frac{1}{4}}cdot 8^{frac{15}{4}}=8^{frac{16}{4}}=8^4\\2); frac{20^{log_25}}{10^{log_25}}=(frac{20}{10})^{log_25}=2^{log_25}=5$