Question

Вычислите. Корни n степени

Answer 1

$\displaystyle \frac{\sqrt[3]{36}\sqrt[4]{9} }{\sqrt[6]{24} }=\frac{\sqrt[12]{36^4}\sqrt[12]{9^3} }{\sqrt[6]{24} }=\frac{\sqrt[12]{36^4*9^3} }{\sqrt[6]{24} }=\frac{\sqrt[12]{36*324^3} }{\sqrt[6]{24} }=\frac{\sqrt[12]{36*324^3} }{\sqrt[6]{24} }*\frac{\sqrt[6]{24^5} }{\sqrt[6]{24^5} }=\\ \\ \\ \frac{\sqrt[12]{36*324^3}\sqrt[6]{24^5} }{\sqrt[6]{24}\sqrt[6]{24^5} }=\frac{\sqrt[12]{36*324^3}\sqrt[12]{24^1^0} }{\sqrt[6]{24*24^5} }=\frac{\sqrt[12]{36*324^3*24^1^0} }{24}=3\sqrt[6]{2}$