原文Activated abilities contain a colon. They're generally written "[Cost]: [Effect]." Some keyword abilities (such as equip) are activated abilities and will have colons in their reminder text. An activated mana ability is one that produces mana as it resolves, not one that costs mana to activate. Notably, exerting a creature isn't an activated ability.
原文Harsh Mentor's ability doesn't trigger when an opponent activates an ability of a card in hand (such as cycling) or a card in a graveyard (such as embalm), even if that causes a card to be put onto the battlefield.