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What is the simplest radical form of the expression? (8x5y3)2/3

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ajeigbeibraheem

The simplest radical form of the expression is [tex]\mathbf{40 ^{2/3}x^{{10}/{3}}y^2}[/tex].

What is the simplification of power indices?

When we have indices in the form [tex]\mathbf{ax^{2/3}}[/tex], we are going to find the cube root of the (ax)². This can be mathematically expressed as:

[tex]\mathbf{=(\sqrt[3]{ax})^2 }[/tex]

From the given information:

[tex]\mathbf{=(8x^55y^3)^{2/3}}[/tex]

[tex]\mathbf{=(\sqrt[3]{8x^55y^3} } )^2[/tex]

[tex]\mathbf{=(\sqrt[3]{40x^5y^3} } )^2[/tex]

[tex]= (\sqrt[3]{40x^5} \times \sqrt[3]{y}^3)^2[/tex]

[tex]\mathbf{= 40 ^{2/3}x^{{5*2}/{3}}y^2}[/tex]

[tex]\mathbf{= 40 ^{2/3}x^{{10}/{3}}y^2}[/tex]

Learn more about indices here:

https://brainly.com/question/170984

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