Identify the expressions that are perfect cubes. Select all that apply. \( \begin{array}{l}z^{9} \\ -16 \\ 70 \\ 1 \\ 42 x^{3} \\ y^{6} \\ 27 a^{3} \\ b^{4} \\ p^{3} q^{2} \\ -1\end{array} \)

Perfect cubes are numbers or algebraic expressions that can be written in the form \(x^3\) where \(x\) is any expression. Let's analyze the given options: - \(z^{9} = (z^3)^3\): This is a perfect cube. - \(-16\): This is not a perfect cube (as the cube root of -16 is not an integer). - \(70\): This is not a perfect cube (as the cube root of 70 is not an integer). - \(1 = 1^3\): This is a perfect cube. - \(42x^{3}\): This is not a perfect cube because 42 is not a perfect cube. - \(y^{6} = (y^2)^3\): This is a perfect cube. - \(27a^{3} = (3a)^3\): This is a perfect cube. - \(b^{4}\): This is not a perfect cube as there is no integer \(k\) such that \(b^{4} = k^3\). - \(p^{3}q^{2}\): This is not a perfect cube as \(q^2\) cannot be expressed as \(k^3\). - \(-1 = (-1)^3\): This is a perfect cube. Thus, the expressions that are perfect cubes are: \(z^{9}, 1, y^{6}, 27a^{3}, -1\).