Question

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

Answer 1

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

What is the simplification of power indices?

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

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

From the given information:

$\mathbf{=(8x^55y^3)^{2/3}}$

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

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

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

$\mathbf{= 40 ^{2/3}x^{{5*2}/{3}}y^2}$

$\mathbf{= 40 ^{2/3}x^{{10}/{3}}y^2}$

Learn more about indices here:

brainly.com/question/170984

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