Question

Which is greater $(150{)}^{300}$ or $(20000{)}^{100}\times (100{)}^{100}$?

Answer 1

$(20000{)}^{100}\times (100{)}^{100}=2^{100}\times (100{)}^{200}\times (100{)}^{200}\times (100{)}^{100}=(2^{1/3}{)}^{300}\times (100{)}^{300}$

$\Rightarrow (20000{)}^{100}\times (100{)}^{100}=(100\sqrt[3]{32}{)}^{300}$

As $100\left(\sqrt[3]{32}\right)<150$

$\therefore (150{)}^{300}$ is greater.