Fill in the missing coordinate in each ordered pair so that the pair is a solution of \( y=-3^{x} \). \[ (4,-81 \] \( \left(\boxed{-2},-\frac{1}{9}\right) \) \[ \left(-1, \frac{-\frac{1}{3}}{}\right) \] d \( \square \) \( ,-243) \) Submit View next step

To fill in the missing coordinate in each ordered pair that solves the equation \( y = -3^{x} \), let’s calculate them one by one! For the first pair, \((4, -81)\): Plugging in \( x = 4 \) gives us \( y = -3^{4} = -81\). This one fits perfectly! For the second pair, \(\left(\boxed{-2}, -\frac{1}{9}\right)\): Here, substituting \( x = -2 \) yields \( y = -3^{-2} = -\frac{1}{9}\). So the boxed value is indeed \(-2\)! For the third pair, \((-1, \frac{-\frac{1}{3}}{})\): When \( x = -1 \), we find \( y = -3^{-1} = -\frac{1}{3} \). Thus, the blank should be filled with \(-\frac{1}{3}\). Finally, for the last pair, \((d, -243)\): Setting \( -243 = -3^{d} \) gives \( 3^{d} = 243 \), and since \( 243 = 3^{5} \), we find that \( d = 5 \). So the filled ordered pairs are \((4, -81)\), \((-2, -\frac{1}{9})\), \((-1, -\frac{1}{3})\), and \((5, -243)\). What a journey through the powers of three!