Simplify. \( \sqrt[5]{x^{10} y^{30} z^{25}} \) \( x^{[?]} y \)

Let's break it down! The expression \( \sqrt[5]{x^{10} y^{30} z^{25}} \) can be simplified by using the properties of exponents. You can distribute the fifth root across all terms: \[ \sqrt[5]{x^{10}} \cdot \sqrt[5]{y^{30}} \cdot \sqrt[5]{z^{25}}. \] Now, simplify each component: \[ \sqrt[5]{x^{10}} = x^{10/5} = x^2, \quad \sqrt[5]{y^{30}} = y^{30/5} = y^6, \quad \text{and} \quad \sqrt[5]{z^{25}} = z^{25/5} = z^5. \] Putting it all together: \[ \sqrt[5]{x^{10} y^{30} z^{25}} = x^2 y^6 z^5. \] Now, we're looking for the expression in the form \( x^{[?]} y \). So, we can rewrite \( x^2 y^6 z^5 \) as: \[ x^2 y^6 = x^2 (y^5 y) = x^2 y^5 y = x^2 y^{1}. \] This means \( x^{[?]} = x^2 \), thus the answer for the exponent is 2. So: \( x^{2} y \) where the missing exponent is 2!