For example, I attack with typhoid rats. Rats goes unblocked. I then try to ninjutsu ink-eyes, servant of oni. Can the opponent stop the ninjutsu by path to exile the rats in response to the ninjutsu?
In general, no. After blockers are declared, the active player (here, you) gets priority to activate abilities, including ninjutsu (C.R. 702.48a). And while you're activating an ability (such as ninjutsu), no player has priority, so no other player can cast spells or activate abilities (including those that would keep you from paying the ability's costs) (C.R. 601.2a-i and 602.2a-b have no priority window until the ability is activated; C.R. 116.1a-b). It follows that if you return a creature to its owner's hand as you pay the cost of ninjutsu (C.R. 702.48a), that creature will leave the battlefield before any player gets priority again (e.g., to cast spells such as Path to Exile) (C.R. 701.16a, 116.1a). See also this thread, this thread, this thread, and this thread.
Also, you can activate the ninjutsu ability in response to Path to Exile as you can to almost any other spell (C.R. 116.7). And once you return Typhoid Rats to its owner's hand this way, Typhoid Rats will be an illegal target for Path to Exile (C.R. 608.2b). Note, however, that the opponent generally need not wait to cast Path to Exile until after blockers are declared, but can do so earlier (e.g., after attackers are declared but before blockers are declared).
For example, I attack with typhoid rats. Rats goes unblocked. I then try to ninjutsu ink-eyes, servant of oni. Can the opponent stop the ninjutsu by path to exile the rats in response to the ninjutsu?
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Also, you can activate the ninjutsu ability in response to Path to Exile as you can to almost any other spell (C.R. 116.7). And once you return Typhoid Rats to its owner's hand this way, Typhoid Rats will be an illegal target for Path to Exile (C.R. 608.2b). Note, however, that the opponent generally need not wait to cast Path to Exile until after blockers are declared, but can do so earlier (e.g., after attackers are declared but before blockers are declared).
Nexus MTG News // Nexus - Magic Art Gallery // MTG Dual Land Color Ratios Analyzer // MTG Card Drawing Odds Calculator
Want to play a UW control deck in modern, but don't have jace or snaps?
Please come visit us at the Emeria Titan control thread