Question

ayudenme porfavor . la resolucion

Answer 1

$R= \sqrt[13]{ \frac{45^8 \cdot75^{11}\cdot225^7}{3^{25}\cdot5^{28}} } =\sqrt[13]{ \frac{(3\cdot3\cdot5)^8 \cdot(5\cdot5\cdot3)^{11}\cdot(5\cdot5\cdot3\cdot3)^7}{3^{25}\cdot5^{28}} }\\=\sqrt[13]{ \frac{(3^2\cdot5)^8 \cdot(5^2\cdot3)^{11}\cdot(5^2\cdot3^2)^7}{3^{25}\cdot5^{28}} }=\sqrt[13]{ \frac{3^{16}\cdot5^8 \cdot5^{22}\cdot3^{11}\cdot5^{14}\cdot3^{14}}{3^{25}\cdot5^{28}} }\\=\sqrt[13]{ \frac{3^{16+11+14} \cdot5^{8+22+14}}{3^{25}\cdot5^{28}} }$
$=\sqrt[13]{ \frac{3^{41} \cdot5^{44}}{3^{25}\cdot5^{28}} }= \sqrt[13]{3^{41-25}\cdot 5^{44-28}} = \sqrt[13]{3^{41-25}\cdot 5^{44-28}}= \\ \sqrt[13]{3^{16}\cdot5^{16}} =3\cdot5 \sqrt[13]{3^3\cdot5^3}=15 \sqrt[13]{3375}$

Saludos!