Factor completely. \[ -47 x^{3} y^{2} z+42 x^{7} y^{6} \]

To factor the expression \( -47 x^{3} y^{2} z + 42 x^{7} y^{6} \), we start by identifying the greatest common factor (GCF) of the two terms. The coefficients are -47 and 42; their GCF is 1. For the variables, we look for the lowest power of each variable present in both terms. Among \( x^{3} \) and \( x^{7} \), the lowest is \( x^{3} \). Among \( y^{2} \) and \( y^{6} \), the lowest is \( y^{2} \). The variable \( z \) appears only in the first term, so we cannot include it in the GCF. Thus, the GCF is \( x^{3} y^{2} \). Now we factor out the GCF: \[ -47 x^{3} y^{2} z + 42 x^{7} y^{6} = x^{3} y^{2} (-47 z + 42 x^{4} y^{4}). \] So the completely factored form is: \[ x^{3} y^{2} (-47 z + 42 x^{4} y^{4}). \]