Let x, y, s, t, m, n be real numbers, where \(s \not = 0\). Suppose that xs = yt and ms = nt. Since xs = yt, xsn = ytn. Since ms = nt, ysm = ynt. So xsn = ytn = ysm. So xsn = ysm. Since s is non-zero, we can divide both sides of the equation by s, to give us xn = ym. This is what we needed to show.