Question

Корень 6 степени, √m^3n^4/192 : корень 6степени √ m^15/3n^5

Answer 1

$\sqrt[6]{ \frac{m^3n^4}{192}}:\sqrt[6]{ \frac{m^{15}}{3n^{5}}}=\sqrt[6]{ \frac{m^3n^4}{192}: \frac{m^{15}}{3n^{5}}}=\sqrt[6]{ \frac{m^3n^4}{192}* \frac{3n^{5}}{m^{15}}}=\sqrt[6]{ \frac{n^9}{64m^{12}}}= \\ =\sqrt[6]{ \frac{n^6*n^3}{2^6(m^2)^6}}= \frac{n*\sqrt[6]{n^3}}{2m^2}=\frac{n \sqrt{n}}{2m^2}$