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The exploit ability is featured in the Silumgar clan (blue-black). When a creature with exploit enters the battlefield you may choose to (or not to) sacrifice a creature. This decision is made when the exploit ability resolves - that is, the ability goes on the stack, and once priority is passed, the exploit ability resolves without use of the stack (i.e., your decision to then sacrifice a creature or not is made without the stack, but only after priority has passed).
You may choose to sacrifice any creature you control, including the creature with the exploit ability itself. If you do choose to sacrifice a creature using the exploit ability, there will be some benefit resulting from that action - you only receive this benefit if you sacrifice the creature using the exploit ability - any other sacrifice of a creature will not trigger (including the exploit ability of a different creature).
The Formidable mechanic is featured in the Atarka clan (red-green). Formidable is an ability word, and so the effect of each formidable ability is different; however, each formidable ability looks at the total power of all creatures you control and whether that total is 8 or more. In calculating the total power of creatures you control, negative power creatures would subtract from the total power.
There are two types of Formidable - those with "intervening if" clauses and those with activated abilities. For activated abilities, the creatures you control must have a total power of 8 or higher in order to activate that ability. Once the ability has been activated, any response to reduce your total power below 8 does not affect the resolution of the activated ability. Formidable abilities with the intervening if clause checks the formidable condition twice - once when the ability triggers, and once when the ability resolves. If you still have formidable upon resolution, the formidable ability will resolve; if you no longer have 8 total power of higher upon resolution, the ability will not resolve.
The Megamorph mechanic functions nearly the same as the Morph mechanic from Khans of Tarkir, but when a creature is turned face up for its Megamorph cost you put a +1/+1 counter onto it. A creature with megamorph can be cast face down for 3 colorless mana and will be a 2/2 creature unless and until it is turned face up. A creature with megamorph that is turned face up using some other means (e.g., paying its casting cost to turn face up when manifested) will not get a +1/+1 counter.
Turning a creature face up does not use the stack and therefore cannot be responded to. Further, using the megamorph mechanic to turn a creature face up will result in that creature having a +1/+1 counter on it before any player can respond. Any triggers that occur upon utilizing the megamorph ability will still use the stack. Creatures being turned face up are not entering the battlefield, nor are they considered new creatures.
Face-down creatures can attack and block, they can be targetted by spells and abilities, they can be enchanted by Auras and equipped by Equipment - they are creatures like any other. Although you can look at your face-down cards at any time, you must reveal a face-down creature to all players to show them it was a creature with megamorph; this is true if the card is going back to your hand, into exile, into your graveyard or anywhere else - and further must be revealed if the game ends.
The Bolster action, featured in the Dromoka clan (green-white) in Dragons of Tarkir (DTK), has not changed since Fate Reforged. Bolster is a keyword action; accompanying the keyword will be a number which tells you how many +1/+1 counters will be created from the action. When a spell or creature with Bolster resolves, the Bolster action is completed without using the stack. The creature receives the counters when you Bolster, not when you cast the spell/creature.
To clarify in the instance of the Bolster action on a creature: the Bolster trigger does use the stack, but once priority is passed on the action, the action is then completed without use of the stack (e.g., your opponent can kill a creature you control with the bolster ability on the stack, but cannot respond to the action of choosing the creature you control to bolster).
To Bolster, you choose the creature you control with the least toughness; in the event of a tie, you may choose one of those creatures. Bolster does not target a creature.
The aptly-named Dash ability is featured in the Kolaghan clan (black-red) and has not changed since its introduction in Fate Reforged. The dash ability is an alternate casting cost option for the creature. When a creature is dashed, it gains haste and returns to its owner's hand at the beginning of the next end step. Dashing a creature is still casting it - it goes on the stack like a normally casted creature, and may be targeted on the stack the same way (e.g., with a counterspell).
In any event where the creature goes to the graveyard or is exiled from play, the return provision will not trigger. Similarly, if the creature leaves play and comes back into play (e.g., from an Astral Slide effect), the returned instance of the card will not return to hand, but rather will stay on the battlefield.
The Rebound mechanic, featured in the Ojutai clan (white-blue), is returning from its introduction in Rise of the Eldrazi - and its functionality has not changed from its introduction. A spell with rebound successfully cast from your hand is exiled rather than being put into your graveyard. At the beginning of your next upkeep, you may cast the spell again from exile without paying its mana cost. If you have multiple spells rebounding during the same upkeep, you can choose the order you cast those spells.
The rebound ability only works if the spells resolves. If the spell is countered (either by a spell or lack of legal targets), it will not rebound - nor will it go into exile; rather, it would simply land in your graveyard with no effect. If you are unable to cast the spell from exile (e.g., if there are no legal targets), the spell stays in exile.