- MODELACIÓN: Escribir las siguientes raíces en forma de potencia y simplificar cada resultado si es posible. 25. \( \sqrt[5]{x^{5} y^{10}} \) 26. \( \sqrt[3]{w^{3} z^{3}} \) 27. \( \sqrt{4 y^{4}} \) 28. \( \sqrt[6]{64 x^{12} y^{6}} \) 29. \( \sqrt[n]{m^{2 n} x^{n}} \) ‥1) \( 30, \sqrt[4]{7^{8} x^{16} y^{8}} \) 31. \( \sqrt[10]{10^{10} x^{20}} \) 32. \( \sqrt[3]{27 x^{3}} \) 33. \( \sqrt[5]{243 x^{10}} \)

Simplify the expression by following steps: - step0: Solution: \(\left(64x^{12}y^{6}\right)^{\frac{1}{6}}\) - step1: Use the properties of exponents: \(64^{\frac{1}{6}}\left(x^{12}\right)^{\frac{1}{6}}\left(y^{6}\right)^{\frac{1}{6}}\) - step2: Evaluate the power: \(2x^{2}y\) Calculate or simplify the expression \( (7^8 * x^16 * y^8)^(1/4) \). Simplify the expression by following steps: - step0: Solution: \(\left(7^{8}x^{16}y^{8}\right)^{\frac{1}{4}}\) - step1: Use the properties of exponents: \(\left(7^{8}\right)^{\frac{1}{4}}\left(x^{16}\right)^{\frac{1}{4}}\left(y^{8}\right)^{\frac{1}{4}}\) - step2: Evaluate the power: \(7^{2}x^{4}y^{2}\) - step3: Evaluate the power: \(49x^{4}y^{2}\) Calculate or simplify the expression \( (243 * x^10)^(1/5) \). Simplify the expression by following steps: - step0: Solution: \(\left(243x^{10}\right)^{\frac{1}{5}}\) - step1: Use the properties of exponents: \(243^{\frac{1}{5}}\left(x^{10}\right)^{\frac{1}{5}}\) - step2: Evaluate the power: \(3x^{2}\) Calculate or simplify the expression \( (w^3 * z^3)^(1/3) \). Simplify the expression by following steps: - step0: Solution: \(\left(w^{3}z^{3}\right)^{\frac{1}{3}}\) - step1: Use the properties of exponents: \(\left(w^{3}\right)^{\frac{1}{3}}\left(z^{3}\right)^{\frac{1}{3}}\) - step2: Evaluate the power: \(wz\) Calculate or simplify the expression \( (x^5 * y^10)^(1/5) \). Simplify the expression by following steps: - step0: Solution: \(\left(x^{5}y^{10}\right)^{\frac{1}{5}}\) - step1: Use the properties of exponents: \(\left(x^{5}\right)^{\frac{1}{5}}\left(y^{10}\right)^{\frac{1}{5}}\) - step2: Evaluate the power: \(xy^{2}\) Calculate or simplify the expression \( (10^10 * x^20)^(1/10) \). Simplify the expression by following steps: - step0: Solution: \(\left(10^{10}x^{20}\right)^{\frac{1}{10}}\) - step1: Use the properties of exponents: \(\left(10^{10}\right)^{\frac{1}{10}}\left(x^{20}\right)^{\frac{1}{10}}\) - step2: Evaluate the power: \(10x^{2}\) Calculate or simplify the expression \( (27 * x^3)^(1/3) \). Simplify the expression by following steps: - step0: Solution: \(\left(27x^{3}\right)^{\frac{1}{3}}\) - step1: Use the properties of exponents: \(27^{\frac{1}{3}}\left(x^{3}\right)^{\frac{1}{3}}\) - step2: Evaluate the power: \(3x\) Calculate or simplify the expression \( (4 * y^4)^(1/2) \). Simplify the expression by following steps: - step0: Solution: \(\left(4y^{4}\right)^{\frac{1}{2}}\) - step1: Use the properties of exponents: \(4^{\frac{1}{2}}\left(y^{4}\right)^{\frac{1}{2}}\) - step2: Evaluate the power: \(2y^{2}\) Calculate or simplify the expression \( (m^(2*n) * x^n)^(1/n) \). Simplify the expression by following steps: - step0: Solution: \(\left(m^{2n}x^{n}\right)^{\frac{1}{n}}\) - step1: Multiply the terms: \(\left(\left(m^{2}x\right)^{n}\right)^{\frac{1}{n}}\) - step2: Transform the expression: \(\left(m^{2}x\right)^{n\times \frac{1}{n}}\) - step3: Multiply the terms: \(m^{2}x\) Aquí están las raíces escritas en forma de potencia y simplificadas: 25. \( \sqrt[5]{x^{5} y^{10}} = xy^{2} \) 26. \( \sqrt[3]{w^{3} z^{3}} = wz \) 27. \( \sqrt{4 y^{4}} = 2y^{2} \) 28. \( \sqrt[6]{64 x^{12} y^{6}} = 2x^{2}y \) 29. \( \sqrt[n]{m^{2 n} x^{n}} = m^{2}x \) 30. \( \sqrt[4]{7^{8} x^{16} y^{8}} = 49x^{4}y^{2} \) 31. \( \sqrt[10]{10^{10} x^{20}} = 10x^{2} \) 32. \( \sqrt[3]{27 x^{3}} = 3x \) 33. \( \sqrt[5]{243 x^{10}} = 3x^{2} \) Si necesitas más ayuda o aclaraciones, no dudes en preguntar.