Preheat the oven to 375°. Line a large baking sheet with parchment paper.
To a large bowl, add butter, granulated sugar, light brown sugar, eggs, and vanilla. Using a hand mixer on medium speed, mix until incorporated.
Mix in flour, baking powder, salt, and baking soda until blended.
Fold in rainbow chips and chocolate chips.
Using a 2-tablespoon scoop, drop dough onto the lined baking sheet, leaving 1-2 inches in between each cookie. Use the bottom of a glass to slightly flatten each scoop of dough. (These cookies don't spread so they will retain the shape you have them in prior to baking.)
Bake for 8-10 minutes, or until the edges are lightly golden. Let the cookies cool for a minute before transferring to a wire rack to cool completely.