1. The problem asks whether the expression $(q^2-2)x^2(-9x^6y^7+11)$ can be written as $x^2[(q^2-2)(-9x^6y^7+11)]$. 2. Start by distributing $x^2$ inside the parentheses in the second expression: $$x^2[(q^2-2)(-9x^6y^7+11)] = x^2 \cdot (q^2-2)(-9x^6y^7+11)$$ 3. Since multiplication is associative and commutative for these terms, we can rearrange the multiplication as: $$(q^2-2) x^2 (-9x^6y^7+11)$$ 4. This matches the original expression exactly. 5. Therefore, yes, the expression $(q^2-2)x^2(-9x^6y^7+11)$ can indeed be written as $x^2[(q^2-2)(-9x^6y^7+11)]$ without changing its value.