@ Escribe cada radical en la forma más simple posil \( \begin{array}{ll}\text { a) } \sqrt[3]{a^{6}} & \begin{array}{ll}\text { d) } \sqrt{16 v^{6} w^{9}}= & \text { b) } \sqrt[3]{m^{4} n^{6}}= \\ \text { g) } \sqrt{\frac{125 x^{3} y^{6}}{49 x y}}= & \text { e) } \sqrt[3]{625 x^{2} y^{3}}= \\ \text { i) } \sqrt[5]{\frac{64 x^{6} y^{3}}{5 m^{3}}}= & \text { h) } \sqrt[3]{\frac{100 a^{3} b^{6}}{16 a b}}= \\ & \text { k) } \sqrt[3]{\frac{24 x^{3} y^{6}}{729}}=\end{array}\end{array}> \)

Simplify the expression by following steps: - step0: Solution: \(\sqrt{16v^{6}w^{9}}\) - step1: Rewrite the exponent: \(\sqrt{2^{4}v^{6}w^{8+1}}\) - step2: Expand the expression: \(\sqrt{2^{4}v^{6}w^{8}\times w}\) - step3: Use the properties of radicals: \(\sqrt{2^{4}v^{6}w^{8}}\times \sqrt{w}\) - step4: Simplify the root: \(4w^{4}v^{3}\sqrt{w}\) - step5: Multiply the expression: \(4\sqrt{w}\times v^{3}w^{4}\) - step6: Rearrange the terms: \(4v^{3}w^{4}\sqrt{w}\) Calculate or simplify the expression \( (24^(1/3)*x^(3/3)*y^(6/3)/729^(1/3)) \). Simplify the expression by following steps: - step0: Solution: \(\frac{24^{\frac{1}{3}}x^{\frac{3}{3}}y^{\frac{6}{3}}}{729^{\frac{1}{3}}}\) - step1: Divide the terms: \(\frac{24^{\frac{1}{3}}x^{1}y^{\frac{6}{3}}}{729^{\frac{1}{3}}}\) - step2: Calculate: \(\frac{24^{\frac{1}{3}}xy^{\frac{6}{3}}}{729^{\frac{1}{3}}}\) - step3: Divide the terms: \(\frac{24^{\frac{1}{3}}xy^{2}}{729^{\frac{1}{3}}}\) - step4: Factor the expression: \(\frac{3^{\frac{1}{3}}\times 2xy^{2}}{3^{\frac{1}{3}}\times 243^{\frac{1}{3}}}\) - step5: Reduce the fraction: \(\frac{2xy^{2}}{243^{\frac{1}{3}}}\) - step6: Simplify: \(\frac{2xy^{2}}{3\sqrt[3]{9}}\) - step7: Calculate: \(\frac{2\sqrt[3]{9^{2}}\times xy^{2}}{3^{3}}\) - step8: Evaluate the power: \(\frac{2\sqrt[3]{81}\times xy^{2}}{27}\) Calculate or simplify the expression \( \sqrt(125*x^(3)*y^(6)/49*x*y) \). Simplify the expression by following steps: - step0: Solution: \(\sqrt{\frac{125x^{3}y^{6}}{49}xy}\) - step1: Multiply the terms: \(\sqrt{\frac{125x^{4}y^{7}}{49}}\) - step2: Use the properties of radicals: \(\frac{\sqrt{125x^{4}y^{7}}}{\sqrt{49}}\) - step3: Simplify the expression: \(\frac{5y^{3}x^{2}\sqrt{5y}}{7}\) - step4: Simplify: \(\frac{5x^{2}y^{3}\sqrt{5y}}{7}\) Calculate or simplify the expression \( (m^(4/3)*n^(6/3)) \). Simplify the expression by following steps: - step0: Solution: \(\left(m^{\frac{4}{3}}n^{\frac{6}{3}}\right)\) - step1: Evaluate: \(m^{\frac{4}{3}}n^{\frac{6}{3}}\) - step2: Divide the terms: \(m^{\frac{4}{3}}n^{2}\) - step3: Simplify: \(m\sqrt[3]{m}\times n^{2}\) Calculate or simplify the expression \( a^(6/3) \). Simplify the expression by following steps: - step0: Solution: \(a^{\frac{6}{3}}\) - step1: Divide the terms: \(a^{2}\) Calculate or simplify the expression \( (625^(1/3)*x^(2/3)*y) \). Simplify the expression by following steps: - step0: Solution: \(\left(625^{\frac{1}{3}}x^{\frac{2}{3}}y\right)\) - step1: Evaluate: \(625^{\frac{1}{3}}x^{\frac{2}{3}}y\) - step2: Simplify: \(5\sqrt[3]{5}\times x^{\frac{2}{3}}y\) - step3: Calculate: \(5\sqrt[3]{5x^{2}}\times y\) Calculate or simplify the expression \( (64^(1/5)*x^(6/5)*y^(3/5)/5^(1/5)*m^(3/5)) \). Simplify the expression by following steps: - step0: Solution: \(\left(\frac{64^{\frac{1}{5}}x^{\frac{6}{5}}y^{\frac{3}{5}}}{5^{\frac{1}{5}}}\times m^{\frac{3}{5}}\right)\) - step1: Evaluate: \(\frac{64^{\frac{1}{5}}x^{\frac{6}{5}}y^{\frac{3}{5}}}{5^{\frac{1}{5}}}\times m^{\frac{3}{5}}\) - step2: Multiply the terms: \(\frac{64^{\frac{1}{5}}x^{\frac{6}{5}}y^{\frac{3}{5}}m^{\frac{3}{5}}}{5^{\frac{1}{5}}}\) - step3: Simplify: \(\frac{2x\sqrt[5]{2xy^{3}m^{3}}}{5^{\frac{1}{5}}}\) - step4: Simplify: \(\frac{2x\sqrt[5]{2xy^{3}m^{3}}}{\sqrt[5]{5}}\) - step5: Calculate: \(\frac{2x\sqrt[5]{1250xy^{3}m^{3}}}{5}\) Calculate or simplify the expression \( (100^(1/3)*a^(3/3)*b^(6/3)/16^(1/3)*a^(1/3)*b^(1/3)) \). Simplify the expression by following steps: - step0: Solution: \(\left(\frac{100^{\frac{1}{3}}a^{\frac{3}{3}}b^{\frac{6}{3}}}{16^{\frac{1}{3}}}\times a^{\frac{1}{3}}b^{\frac{1}{3}}\right)\) - step1: Evaluate: \(\frac{100^{\frac{1}{3}}a^{\frac{3}{3}}b^{\frac{6}{3}}}{16^{\frac{1}{3}}}\times a^{\frac{1}{3}}b^{\frac{1}{3}}\) - step2: Divide the terms: \(\frac{100^{\frac{1}{3}}a^{1}b^{\frac{6}{3}}}{16^{\frac{1}{3}}}\times a^{\frac{1}{3}}b^{\frac{1}{3}}\) - step3: Calculate: \(\frac{100^{\frac{1}{3}}ab^{\frac{6}{3}}}{16^{\frac{1}{3}}}\times a^{\frac{1}{3}}b^{\frac{1}{3}}\) - step4: Divide the terms: \(\frac{100^{\frac{1}{3}}ab^{2}}{16^{\frac{1}{3}}}\times a^{\frac{1}{3}}b^{\frac{1}{3}}\) - step5: Divide the terms: \(\frac{25^{\frac{1}{3}}ab^{2}}{4^{\frac{1}{3}}}\times a^{\frac{1}{3}}b^{\frac{1}{3}}\) - step6: Multiply the terms: \(\frac{25^{\frac{1}{3}}a^{\frac{4}{3}}b^{2}}{4^{\frac{1}{3}}}\times b^{\frac{1}{3}}\) - step7: Multiply the terms: \(\frac{25^{\frac{1}{3}}a^{\frac{4}{3}}b^{2}\times b^{\frac{1}{3}}}{4^{\frac{1}{3}}}\) - step8: Multiply the terms: \(\frac{25^{\frac{1}{3}}a^{\frac{4}{3}}b^{\frac{7}{3}}}{4^{\frac{1}{3}}}\) - step9: Simplify: \(\frac{ab^{2}\sqrt[3]{25ab}}{4^{\frac{1}{3}}}\) - step10: Simplify: \(\frac{ab^{2}\sqrt[3]{25ab}}{\sqrt[3]{4}}\) - step11: Calculate: \(\frac{ab^{2}\sqrt[3]{400ab}}{2^{2}}\) - step12: Evaluate the power: \(\frac{ab^{2}\sqrt[3]{400ab}}{4}\) Aquí están los radicales simplificados: a) \( \sqrt[3]{a^{6}} = a^{2} \) b) \( \sqrt[3]{m^{4} n^{6}} = m\sqrt[3]{m} \cdot n^{2} \) d) \( \sqrt{16 v^{6} w^{9}} = 4v^{3}w^{4}\sqrt{w} \) e) \( \sqrt[3]{625 x^{2} y^{3}} = 5\sqrt[3]{5x^{2}} \cdot y \) g) \( \sqrt{\frac{125 x^{3} y^{6}}{49 x y}} = \frac{5x^{2}y^{3}\sqrt{5y}}{7} \) h) \( \sqrt[3]{\frac{100 a^{3} b^{6}}{16 a b}} = \frac{ab^{2}\sqrt[3]{400ab}}{4} \) i) \( \sqrt[5]{\frac{64 x^{6} y^{3}}{5 m^{3}}} = \frac{2x\sqrt[5]{1250xy^{3}m^{3}}}{5} \) k) \( \sqrt[3]{\frac{24 x^{3} y^{6}}{729}} = \frac{2\sqrt[3]{81} \cdot xy^{2}}{27} \) Si necesitas más ayuda o aclaraciones, no dudes en preguntar.