From the Super Mario Wiki, the Mario encyclopedia
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Mario & Luigi series
Mario & Luigi: Superstar Saga / Mario & Luigi: Superstar Saga + Bowser's Minions
Red Peppers boost attack power (and give the Heavy G status effect) in Mario & Luigi: Superstar Saga and its 3DS remake, giving more power to Mario and Luigi's attacks. The status is indicated by a red burst with an arrow pointing up next to Mario and Luigi's HP.
Mario & Luigi: Partners in Time
Red Peppers appear again in Mario & Luigi: Partners in Time, although they affect both fighters currently active and do not give the Heavy G status. POW-Up is indicated by an expanding red circle around the character. Certain enemies can also raise their own attack power by becoming enraged (usually due to low HP), like Bullies.
Mario & Luigi: Bowser's Inside Story / Mario & Luigi: Bowser's Inside Story + Bowser Jr.'s Journey
The POW-Up status effect also appears in Mario & Luigi: Bowser's Inside Story and Mario & Luigi: Bowser's Inside Story + Bowser Jr.'s Journey, with the same effects as the previous games. It can be received by Bowser if he inhales the meat seen during the second Midbus battle.
Mario & Luigi: Dream Team
POW-Up returns in Mario & Luigi: Dream Team. By using a Gold-Guard Badge combo, Mario and Luigi can increase their attack power. This also affects enemies, which can be used by a Risk-Silver Badge combo.
Mario & Luigi: Paper Jam
Paper Mario series
Paper Mario: The Thousand-Year Door
In Paper Mario: The Thousand-Year Door, several items and the Crystal Star power called Power Lift can raise attack power. The "Attack is boosted!" status is indicated by an angry face above Mario or his partner. Charging also boosts attack power for the next attack only; this is indicated by the affected character changing color repeatedly in a pulsing fashion. Enemies can have this status effect, also, by taking up a turn to charge.
Paper Mario: Sticker Star
In Paper Mario: Sticker Star, it acts like Paper Mario: The Thousand-Year Door. Mario can obtain it with a Leaf sticker, and Sombrero Guys can give it to other enemies. The player can also use the Boom Box to double their attack.