Question

ayuda por favor ...............

Answer 1

1. 1.62
2. $1.59x^{\frac{2}{3}}y^{\frac{1}{3}}$
3. $m^{\frac{1}{2}}n^{\frac{3}{2}}$
4. $5.72m^{\frac{1}{6}}y^{\frac{1}{2}}$
5. 1.41

⭐Explicación paso a paso:

 

Resolvemos cada una de las raíces sabiendo que se cumple la siguiente propiedad:

$\boxed {\sqrt[n]{x}=x^{\frac{1}{n}}}$

   

1) $\sqrt[5]{2}*\sqrt{2}$

$(2)^{\frac{1}{5}}*2^{\frac{1}{2}} =1.15*1.414=1.62$

 

2) $\sqrt[6]{16x^{2}y^{2} }$

$16^{\frac{1}{6}}(x^{4})^{\frac{1}{6} } (y^{2} )^{\frac{1}{6}} =1.59x^{\frac{2}{3}}y^{\frac{1}{3}}$

 

3) $\sqrt[8]{m^{4}n^{12} }$

$(m^{4})^{\frac{1}{8}}(n^{12})^{\frac{1}{8}} =m^{\frac{1}{2}}n^{\frac{3}{2}}$

 

4) $\sqrt[3]{\sqrt{9my^{3}}}$

$[(9)^{\frac{1}{2}}]^{\frac{1}{3}}[m^{\frac{1}{2}}]^{\frac{1}{3}}[y^{3}^{\frac{1}{2}}]^{\frac{1}{3}}=5.72m^{\frac{1}{6}}y^{\frac{1}{2}}$

 

5) $\sqrt[5]{\frac{7^{2} }{3^{2} } }$

$\frac{(7^{2})^{\frac{1}{5}}}{(3^{2})^{\frac{1}{5}}} =\frac{2^{\frac{2}{5}}}{3^{\frac{2}{5}}}=\frac{2.18}{1.55}=\frac{218}{255}=1.41$