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Determine, without a calculator, which is greater 4^100 or 6^75

$\begin{array}{|rcl|cl|} \hline && 4^{100} && 6^{75} \\ &=& 4^{4\cdot 25} &=& 6^{3\cdot 25} \\ &=& \left(4^4\right)^{25} &=& \left(6^3\right)^{25} \\ &=& 256^{25} &=& 216^{25} \\ \hline \end{array}$

$\text{So $4^{100}$ is greater than $6^{75}$ }$