(1) RAZONAMIENTO. Cdicular las siguientes raices aplicando las propiedades de los'radicales: 13. \( \sqrt{(-5)^{2}} \) 14. \( \sqrt[3]{-729 x^{6}} \) 15. \( \sqrt[4]{16 a^{8} b^{4}} \) 16. \( \sqrt[5]{3.125 m^{10} n^{5}} \) 17. \( \sqrt[2]{64 x^{10} y^{8} z^{6}} \) 18. \( \sqrt[3]{-27 x^{-6} y^{9}} \) 19. \( \sqrt{\frac{9 y^{8}}{m^{12}}} \) 20. \( \frac{\sqrt{12 a^{4} b^{6}}}{1 \sqrt{3 b^{2}}} \) \( : 27 \cdot \sqrt[5]{\frac{128 x^{15} y^{20}}{4 z^{10}}} \) 22. \( \sqrt[3]{4 \sqrt{4 m^{6}}} \) 23. \( \sqrt[4]{\sqrt[2]{m^{16} y^{24} z^{8}}} \) 24. \( \sqrt{x^{2} \sqrt[3]{64 y^{6}}} \)

Simplify the expression by following steps: - step0: Solution: \(\sqrt{x^{2}\sqrt[3]{64y^{6}}}\) - step1: Simplify the root: \(\sqrt{x^{2}\times 4y^{2}}\) - step2: Calculate: \(\sqrt{4x^{2}y^{2}}\) - step3: Transform the expression: \(\sqrt{\left(2xy\right)^{2}}\) - step4: Simplify the root: \(2xy\) Calculate or simplify the expression \( \sqrt[4]{16 * a^8 * b^4} \). Simplify the expression by following steps: - step0: Solution: \(\sqrt[4]{16a^{8}b^{4}}\) - step1: Transform the expression: \(\sqrt[4]{\left(2a^{2}b\right)^{4}}\) - step2: Simplify the root: \(2a^{2}b\) Calculate or simplify the expression \( \sqrt[3]{-27 * x^{-6} * y^{9}} \). Simplify the expression by following steps: - step0: Solution: \(\sqrt[3]{-27x^{-6}y^{9}}\) - step1: Rewrite the expression: \(\sqrt[3]{-\frac{27y^{9}}{x^{6}}}\) - step2: Use the properties of radicals: \(-\sqrt[3]{\frac{27y^{9}}{x^{6}}}\) - step3: Simplify the expression: \(-\frac{3y^{3}}{x^{2}}\) Calculate or simplify the expression \( \sqrt(9 * y^{8} / m^{12}) \). Simplify the expression by following steps: - step0: Solution: \(\sqrt{\frac{9y^{8}}{m^{12}}}\) - step1: Use the properties of radicals: \(\frac{\sqrt{9y^{8}}}{\sqrt{m^{12}}}\) - step2: Simplify the expression: \(\frac{3y^{4}}{m^{6}}\) Calculate or simplify the expression \( 27 * \sqrt[5]{(128 * x^{15} * y^{20}) / (4 * z^{10})} \). Simplify the expression by following steps: - step0: Solution: \(27\sqrt[5]{\frac{128x^{15}y^{20}}{4z^{10}}}\) - step1: Divide the terms: \(27\sqrt[5]{\frac{32x^{15}y^{20}}{z^{10}}}\) - step2: Simplify the root: \(27\times \frac{2x^{3}y^{4}}{z^{2}}\) - step3: Multiply the terms: \(\frac{27\times 2x^{3}y^{4}}{z^{2}}\) - step4: Multiply the terms: \(\frac{54x^{3}y^{4}}{z^{2}}\) Calculate or simplify the expression \( \sqrt[5]{3.125 * m^{10} * n^{5}} \). Simplify the expression by following steps: - step0: Solution: \(\sqrt[5]{3.125m^{10}n^{5}}\) - step1: Rewrite the expression: \(\sqrt[5]{\frac{25m^{10}n^{5}}{8}}\) - step2: Use the properties of radicals: \(\frac{\sqrt[5]{25m^{10}n^{5}}}{\sqrt[5]{8}}\) - step3: Simplify the expression: \(\frac{\sqrt[5]{25}\times nm^{2}}{\sqrt[5]{8}}\) - step4: Simplify: \(\frac{\sqrt[5]{100}\times nm^{2}}{2}\) Calculate or simplify the expression \( \sqrt((-5)^2) \). Calculate the value by following steps: - step0: Calculate: \(\sqrt{\left(-5\right)^{2}}\) - step1: Simplify the root: \(\left|-5\right|\) - step2: Calculate the absolute value: \(5\) Calculate or simplify the expression \( (\sqrt(12 * a^{4} * b^{6}) / (1 * \sqrt(3 * b^{2}))) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\sqrt{12a^{4}b^{6}}}{\left(1\times \sqrt{3b^{2}}\right)}\) - step1: Remove the parentheses: \(\frac{\sqrt{12a^{4}b^{6}}}{1\times \sqrt{3b^{2}}}\) - step2: Simplify the root: \(\frac{\sqrt{12a^{4}b^{6}}}{1\times \sqrt{3}\times b}\) - step3: Simplify the root: \(\frac{2\sqrt{3}\times b^{3}a^{2}}{1\times \sqrt{3}\times b}\) - step4: Calculate: \(\frac{2\sqrt{3}\times b^{3}a^{2}}{\sqrt{3}\times b}\) - step5: Reduce the fraction: \(2b^{2}a^{2}\) Calculate or simplify the expression \( \sqrt[3]{-729 * x^6} \). Simplify the expression by following steps: - step0: Solution: \(\sqrt[3]{-729x^{6}}\) - step1: Use the properties of radicals: \(-\sqrt[3]{729x^{6}}\) - step2: Simplify the expression: \(-9x^{2}\) Calculate or simplify the expression \( \sqrt[4]{\sqrt[2]{m^{16} * y^{24} * z^{8}}} \). Simplify the expression by following steps: - step0: Solution: \(\sqrt[4]{\sqrt{m^{16}y^{24}z^{8}}}\) - step1: Simplify the expression: \(\sqrt[4\times 2]{m^{16}y^{24}z^{8}}\) - step2: Multiply the numbers: \(\sqrt[8]{m^{16}y^{24}z^{8}}\) - step3: Transform the expression: \(\sqrt[8]{\left(m^{2}y^{3}z\right)^{8}}\) - step4: Simplify the root: \(m^{2}y^{3}z\) Calculate or simplify the expression \( \sqrt[2]{64 * x^{10} * y^{8} * z^{6}} \). Simplify the expression by following steps: - step0: Solution: \(\sqrt{64x^{10}y^{8}z^{6}}\) - step1: Transform the expression: \(\sqrt{\left(8x^{5}y^{4}z^{3}\right)^{2}}\) - step2: Simplify the root: \(8x^{5}y^{4}z^{3}\) Calculate or simplify the expression \( \sqrt[3]{4 * \sqrt(4 * m^{6})} \). Simplify the expression by following steps: - step0: Solution: \(\sqrt[3]{4\sqrt{4m^{6}}}\) - step1: Simplify the root: \(\sqrt[3]{4\times 2m^{3}}\) - step2: Multiply the numbers: \(\sqrt[3]{8m^{3}}\) - step3: Transform the expression: \(\sqrt[3]{\left(2m\right)^{3}}\) - step4: Simplify the root: \(2m\) Aquí están las soluciones a las raíces solicitadas, aplicando las propiedades de los radicales: 13. \( \sqrt{(-5)^{2}} = 5 \) 14. \( \sqrt[3]{-729 x^{6}} = -9x^{2} \) 15. \( \sqrt[4]{16 a^{8} b^{4}} = 2a^{2}b \) 16. \( \sqrt[5]{3.125 m^{10} n^{5}} = \frac{\sqrt[5]{100} \times nm^{2}}{2} \) 17. \( \sqrt[2]{64 x^{10} y^{8} z^{6}} = 8x^{5}y^{4}z^{3} \) 18. \( \sqrt[3]{-27 x^{-6} y^{9}} = -\frac{3y^{3}}{x^{2}} \) 19. \( \sqrt{\frac{9 y^{8}}{m^{12}}} = \frac{3y^{4}}{m^{6}} \) 20. \( \frac{\sqrt{12 a^{4} b^{6}}}{1 \sqrt{3 b^{2}}} = 2b^{2}a^{2} \) 21. \( 27 \cdot \sqrt[5]{\frac{128 x^{15} y^{20}}{4 z^{10}}} = \frac{54x^{3}y^{4}}{z^{2}} \) 22. \( \sqrt[3]{4 \sqrt{4 m^{6}}} = 2m \) 23. \( \sqrt[4]{\sqrt[2]{m^{16} y^{24} z^{8}}} = m^{2}y^{3}z \) 24. \( \sqrt{x^{2} \sqrt[3]{64 y^{6}}} = 2xy \) Si necesitas más aclaraciones o ejemplos, no dudes en preguntar.