The set of functions {x[superscript q] | q[element of][real numbers set]} is linearly independent over R (with respect to any open subinterval of (0, 8)). The titular result is a corollary for any integer n = 2 (and the domain [0, 8)). Some more accessible proofs of that result are also given. Let F be a finite field of characteristic p and cardinality p[superscript k]. Then the pth-root function F [right arrow] F is a polynomial function of degree at most p[superscript k] - 2 if p[superscript k] ? 2 (resp., the identity function if p[superscript k] = 2). Also, for any integer n = 2, every element of F has an nth root in F if and only if, for each prime number q dividing n, q is not a factor of p[superscript k] - 1. Various parts of this note could find classroom use in courses at various levels, on precalculus, calculus or abstract algebra. A final section addresses educational benefits of such coverage and offers some recommendations to practitioners.