`a) 32^9=(2^5)^9=2^45`
`16^13=(2^4)^13=2^52`
Do `2^45<2^52=>32^9<16^13`
`b) 5^35=(5^5)^7=3125^7`
`2^91=(2^13)^7=8192^7`
Do `8192^7>3125^7=>2^91>5^35`
`c) (-1/16)^100=((1/2)^4)^100=(1/2)^400`
`(-1/2)^500=(1/2)^500`
Do `(1/2)^400<(1/2)^500=>(-1/16)^100<(-1/2)^500`