(0) \( \sqrt{255^{3} p^{10}} \) (3) \( 202 \sqrt{323^{3} y^{10}} \) (5) \( \sqrt{2} \times \sqrt{8} \) (6) \( \sqrt[10]{9 x^{10}+16 x^{10}} \) (9) \( \sqrt{3 m^{3}} \times \sqrt{27 m} \) (11) \( \frac{\sqrt{9 x^{0}}-\sqrt{4 x^{10}}}{5 x^{3}} \)

Simplify the expression by following steps: - step0: Solution: \(\sqrt{255^{3}p^{10}}\) - step1: Rewrite the exponent: \(\sqrt{255^{2+1}p^{10}}\) - step2: Expand the expression: \(\sqrt{255^{2}\times 255p^{10}}\) - step3: Reorder the terms: \(\sqrt{255^{2}p^{10}\times 255}\) - step4: Use the properties of radicals: \(\sqrt{255^{2}p^{10}}\times \sqrt{255}\) - step5: Simplify the root: \(255\sqrt{255}\times p^{5}\) Calculate or simplify the expression \( \sqrt(2) * \sqrt(8) \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{2}\times \sqrt{8}\) - step1: Simplify the root: \(\sqrt{2}\times 2\sqrt{2}\) - step2: Multiply the terms: \(2\times 2\) - step3: Multiply the numbers: \(4\) Calculate or simplify the expression \( \sqrt(9 * x^10 + 16 * x^10) \). Simplify the expression by following steps: - step0: Solution: \(\sqrt{9x^{10}+16x^{10}}\) - step1: Add the terms: \(\sqrt{25x^{10}}\) - step2: Transform the expression: \(\sqrt{\left(5x^{5}\right)^{2}}\) - step3: Simplify the root: \(5x^{5}\) Calculate or simplify the expression \( (\sqrt(9 * x^0) - \sqrt(4 * x^10)) / (5 * x^3) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(\sqrt{9x^{0}}-\sqrt{4x^{10}}\right)}{5x^{3}}\) - step1: Remove the parentheses: \(\frac{\sqrt{9x^{0}}-\sqrt{4x^{10}}}{5x^{3}}\) - step2: Evaluate the power: \(\frac{\sqrt{9\times 1}-\sqrt{4x^{10}}}{5x^{3}}\) - step3: Multiply: \(\frac{\sqrt{9}-\sqrt{4x^{10}}}{5x^{3}}\) - step4: Simplify the root: \(\frac{3-\sqrt{4x^{10}}}{5x^{3}}\) - step5: Simplify the root: \(\frac{3-2x^{5}}{5x^{3}}\) Calculate or simplify the expression \( 202 * \sqrt(323^3 * y^10) \). Simplify the expression by following steps: - step0: Solution: \(202\sqrt{323^{3}y^{10}}\) - step1: Simplify the root: \(202\times 323\sqrt{323}\times y^{5}\) - step2: Multiply the numbers: \(65246\sqrt{323}\times y^{5}\) Calculate or simplify the expression \( \sqrt(3 * m^3) * \sqrt(27 * m) \). Simplify the expression by following steps: - step0: Solution: \(\sqrt{3m^{3}}\times \sqrt{27m}\) - step1: Simplify the root: \(m\sqrt{3m}\times \sqrt{27m}\) - step2: Simplify the root: \(m\sqrt{3m}\times 3\sqrt{3m}\) - step3: Calculate: \(m\times 3\times 3m\) - step4: Multiply the terms: \(9m\times m\) - step5: Calculate: \(9m^{2}\) Here are the simplified results for each expression: 1. **Expression:** \( \sqrt{255^{3} p^{10}} \) **Simplified Result:** \( 255\sqrt{255} \times p^{5} \) 2. **Expression:** \( 202 \sqrt{323^{3} y^{10}} \) **Simplified Result:** \( 65246\sqrt{323} \times y^{5} \) 3. **Expression:** \( \sqrt{2} \times \sqrt{8} \) **Simplified Result:** \( 4 \) 4. **Expression:** \( \sqrt[10]{9 x^{10}+16 x^{10}} \) **Simplified Result:** \( 5x^{5} \) 5. **Expression:** \( \sqrt{3 m^{3}} \times \sqrt{27 m} \) **Simplified Result:** \( 9m^{2} \) 6. **Expression:** \( \frac{\sqrt{9 x^{0}}-\sqrt{4 x^{10}}}{5 x^{3}} \) **Simplified Result:** \( \frac{3-2x^{5}}{5x^{3}} \) If you have any further questions or need additional assistance, feel free to ask!