9. Each of the numbers \(a, b\) and \(с\) is not equal to zero. It is known that the numbers \((-2)^{8} a^{3} b^{3} c^{n-1}\) and \((-3)^{3} a^{2} b^{5} c^{n+1}\) have the same sign. Determine the sign of the number \(a\).
9. Solution. The numbers \((-2)^{8}\) and \((-3)^{9}\) have different signs, the numbers \(b^{3}\) and \(b^{5}\) have the same sign, and the numbers \(c^{n-1}\) and \(c^{n+1}\) also have the same sign, since the difference between the exponents is two, and therefore both exponents are either even or odd simultaneously. Consequently, for the monomials to have the same sign, \(a^{3}\) and \(a^{2}\) must have different signs. This is only possible when the number \(a\) is negative.