Answer:
The cube root of given expression is [tex]6x^3y^6[/tex].
Step-by-step explanation:
The given expression is
[tex]\sqrt[3]{216x^9y^{18}}[/tex]
It can be written as
Use the exponent property: [tex]a^{mn}=(a^m)^n[/tex]
[tex]\sqrt[3]{216x^9y^{18}}=\sqrt[3]{6^3(x^3)^3(y^6)^{3}}[/tex]
[tex]\sqrt[3]{216x^9y^{18}}=\sqrt[3]{(6x^3y^6)^{3}}[/tex]
[tex]\sqrt[3]{216x^9y^{18}}=6x^3y^6[/tex]
Therefore the cube root of given expression is [tex]6x^3y^6[/tex].
