\((i) Taking the natural logarithm of both sides of the equation yⁿ = Ax³, we have:\)

\(n \ln y = \ln A + 3 \ln x\)

This equation is of the form \(Y = mX + C\), where \(Y = \ln y\), \(X = \ln x\), \(m = 3\), and \(C = \ln A\). Therefore, the graph of \(\ln y\) against \(\ln x\) is a straight line.

(ii) Using the given points \((x_1, y_1) = (1.20, 2.58)\) and \((x_2, y_2) = (2.51, 9.49)\), substitute into the equation:

For \((1.20, 2.58)\):

\(n \ln(2.58) = \ln A + 3 \ln(1.20)\)

For \((2.51, 9.49)\):

\(n \ln(9.49) = \ln A + 3 \ln(2.51)\)

Solving these two equations simultaneously, we find:

\(n = 1.70\)

\(A = 2.90\)