Divide x to the 1 half power divided by x to the 2 sevenths power.

Solution:

Given, expression is

x to the 1 half power divided by x to the 2 sevenths power.

Remembering some basic rules,

\(x^{m}/x^{n}\) = \(x^{m-n}\)

\(x\tfrac{m}{n}\) = \(\sqrt[n]{x^{m}}\)

So,

\(x^{1/2}/x^{2/7}\) = \(x^{1/2-2/7}\)

= 1/2 - 2/7

= 7/14 - 4/14

= 3/14

\(x^{1/2-2/7}\) = \(x^{3/14}\)

\(x^{3/14}\) = \(\sqrt[14]{x^{3}}\)

Therefore, \(x^{1/2}/x^{2/7}\) = \(\sqrt[14]{x^{3}}\).

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Divide x to the 1 half power divided by x to the 2 sevenths power.

Summary:

Dividing x to the 1 half power divided by x to the 2 sevenths power, we get \(x^{1/2}/x^{2/7}\) = \(\sqrt[14]{x^{3}}\).