simplify by factoring. assume that all expressions under radicals represent nonnegative numbers. \n\\(…

Explanation:

Step1: Use the property of square roots

$$\sqrt{x^{16}y^{35}}=\sqrt{x^{16}y^{34}\cdot y}$$

Step2: Apply the product rule of square roots

$$\sqrt{x^{16}y^{34}\cdot y}=\sqrt{x^{16}y^{34}}\cdot\sqrt{y}$$

Step3: Simplify $\sqrt{x^{16}y^{34}}$

Since $\sqrt{a^{m}} = a^{\frac{m}{2}}$ (for non - negative (a)), for (x^{16}), (\sqrt{x^{16}}=x^{8}) (because (\frac{16}{2}=8)), and for (y^{34}), (\sqrt{y^{34}} = y^{17}) (because (\frac{34}{2}=17)). So (\sqrt{x^{16}y^{34}}=x^{8}y^{17})

Step4: Combine the results

$$\sqrt{x^{16}y^{34}}\cdot\sqrt{y}=x^{8}y^{17}\sqrt{y}$$

Answer:

(x^{8}y^{17}\sqrt{y})