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The expression cube root of 54x^8y^12 can be written in simplest radical form as

Sagot :

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]

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