Question

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Explanation:

Step1: Recall the definition of a polynomial

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non - negative integer exponents of variables. Let's rewrite the given expression \(\frac{\sqrt[6]{x^{2}}}{5}\). Using the property of radicals \(\sqrt[n]{a^{m}}=a^{\frac{m}{n}}\), we can rewrite \(\sqrt[6]{x^{2}}\) as \(x^{\frac{2}{6}}=x^{\frac{1}{3}}\). So the expression becomes \(\frac{1}{5}x^{\frac{1}{3}}\).

Step2: Check the exponent of the variable

For an expression to be a polynomial, the exponent of the variable must be a non - negative integer. Here, the exponent of \(x\) is \(\frac{1}{3}\), which is a rational number but not an integer. So the expression \(\frac{\sqrt[6]{x^{2}}}{5}\) is not a polynomial.

Answer:

The given expression \(\boldsymbol{\frac{\sqrt[6]{x^{2}}}{5}}\) does not represent a polynomial.