Here is a problem with indices:
1) Show that $2^2 3^3>2^3 3^2$.
* 2) Show that: $$\left(2\times3\times4\times5\times\cdots\times100\times101\right)^2<2\times3^3\times4^3\times5^5\times6^5\times\cdots\times100^{99}\times101^{101}$$
** 3) Prove that:
$$\left(2\times3\times4\times5\times\cdots\times100\times101\right)^2 > 2^3\times3\times4\times5^3\times6^3\times7\times\cdots\times100\times101^3$$
