Respuesta :
Answer:
The simplest radical form of the cubic root is [tex]3x^2y^4\sqrt[3]{2x}[/tex]
Step-by-step explanation:
Cube root of 54x^8y^12
That is:
[tex]\sqrt[3]{54x^8y^12}[/tex]
Can be simplified as:
[tex]\sqrt[3]{54x^8y^12} = \sqrt[3]{54}\sqrt[3]{x^8}\sqrt[3]{y^12}[/tex]
We find each separate simplification, and multiply them:
Cubic root of 54:
[tex]54 = 2*3^3[/tex]
So
[tex]\sqrt[3]{54} = \sqrt[3]{2*3^3} = 3\sqrt[3]{2}[/tex]
Cubic root of x^8
[tex]\sqrt[3]{x^8} = \sqrt[3]{x^6*x^2} = x^2\sqrt[3]{x^2}[/tex]
Cubic root of y^12
[tex]\sqrt[3]{y^{12}} = y^4[/tex]
Multiplying all these terms:
[tex]\sqrt[3]{54}\sqrt[3]{x^8}\sqrt[3]{y^12} = 3\sqrt[3]{2}(x^2\sqrt[3]{x^2})(y^4) = 3x^2y^4\sqrt[3]{2x}[/tex]
The simplest radical form of the cubic root is [tex]3x^2y^4\sqrt[3]{2x}[/tex]
