Question

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

Answer 1

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