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

1. Consider the expression \( z^{9} \). Since \( 9 = 3 \times 3 \), we can write \[ z^{9} = \left(z^3\right)^3, \] which shows it is a perfect cube. 2. For \(-16\), no integer \(a\) exists such that \( a^3 = -16 \). Thus, \(-16\) is not a perfect cube. 3. The number \(70\) is not a perfect cube. 4. The number \(1\) is a perfect cube since \[ 1^3 = 1. \] 5. In \(42x^3\), even though \(x^3\) is a perfect cube, the constant \(42\) is not. Therefore, \(42x^3\) is not a perfect cube. 6. For \(y^{6}\), we note that \[ y^{6} = \left(y^2\right)^3, \] which means it is a perfect cube. 7. In \(27a^3\), recognize that \[ 27 = 3^3. \] Thus, \[ 27a^3 = \left(3a\right)^3, \] making it a perfect cube. 8. The expression \(b^4\) is not a perfect cube since the exponent \(4\) is not a multiple of \(3\). 9. For \(p^3q^2\), although \(p^3\) is a perfect cube, \(q^2\) is not. Hence, \(p^3q^2\) is not a perfect cube. 10. Finally, \(-1\) is a perfect cube because \[ (-1)^3 = -1. \] The expressions that are perfect cubes are: - \( z^{9} \) - \( 1 \) - \( y^{6} \) - \( 27a^{3} \) - \(-1\)