Question

resolver con propiedades de la radicacion para simplificar las expresiones

Answer 1

$\sqrt[3]{ \sqrt[5]{b} } = \sqrt[(3*5)]{b} = \sqrt[15]{b} \\ \\ \\ \sqrt{4x} * \sqrt{20x^3} =2 \sqrt{x} * \sqrt{4*5*x^2*x} =2 \sqrt{x} *2x \sqrt{5x} =4x* \sqrt{x*5x} = \\ = 4x^2* \sqrt{5} \\ \\ \\ \sqrt[3]{ \frac{4xy^3}{256x^4y^2} } = \sqrt[3]{ \frac{4xy^3}{2^8*x^3*x*y^2} } =\sqrt[3]{ \frac{4xy^3}{2^3*2^3*2^2*x^3*x*y^2} }= \frac{y}{2*2*x} * \sqrt[3]{ \frac{4x}{4xy^2} } = \\ \\ =\frac{y}{2*2*x} * \sqrt[3]{ \frac{1}{y^2} }$


$\sqrt{ \sqrt{ \frac{ \sqrt{4a^2b^8} }{6561 a^{16} b^{24} } } } = \sqrt[4]{\frac{ \sqrt{4a^2b^8} }{6561 a^{16} b^{24}}} = \frac{ \sqrt[8]{4a^2b^8}}{ \sqrt[4]{3^8 a^{16} b^{24} } } = \frac{b \sqrt[8]{4a^2} }{3^2a^4b^6} = \frac{ \sqrt[8]{4a^2} }{9a^4b^5}$

Saludos.