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We prove that if a subset of $(\mathbb{F}_q^n)^k$ (with $q$ an odd primepower) avoids a full-rank three-point pattern$\vec{x},\vec{x}+M_1\vec{d},\vec{x}+M_2\vec{d}$ then it is exponentially small,having size at most $3 \cdot c_q^{nk}$ where $0.8414 q \leq c_q \leq 0.9184 q$.This generalizes a theorem of Kova\u{c} and complements results of Berger, Sah,Sawhney and Tidor. As a consequence, we prove that if $3$ is a square in$\mathbb{F}_q$ then subsets of $(\mathbb{F}_q^n)^2$ avoiding equilateraltriangles are exponentially small.

Sets Avoiding Full-Rank Three-Point Patterns in $(\mathbb{F}_q^n)^k$ Are Exponentially Small