Question

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Answer 1

$1)3^{200}=(3^{2})^{100} =9^{100}\\\\2^{300}=(2^{3} )^{100}=8^{100}\\\\9^{100}>8^{100}\\\\\boxed{3^{200}>2^{300}}\\\\\\2)2^{13}*11^{8}=2^{8}*2^{5}*11^{8}=(2^{8}*11^{8})*2^{5}=22^{8}*32\\\\22^{9}=22^{8}*22\\\\22^{8}*32>22^{8}*22\\\\\boxed{2^{13} *11^{8}>22^{9}}\\\\\\3)27^{4}=(3^{3})^{4} = (3^{4})^{3}=81^{3}\\\\11^{6}=(11^{2})^{3}=121^{3}\\\\81^{3}<121^{3}\\\\\boxed{27^{4}<11^{6}} \\\\\\4)126^{12}=(126^{2})^{6} =15876^{6}$

$24^{18}=(24^{3})^{6} =13824^{6}\\\\15876^{6}>13824^{6}\\\\\boxed{126^{12}>24^{18}}$