Which of the following is the simplified form of $\sqrt{x}\cdot \sqrt[7]{x}\cdot \sqrt[7]{x}$ ?
$x^{\frac{3}{7}}$
$x^{\frac{1}{7}}$
$x^{\frac{3}{21}}$
$21\sqrt{x}$

Step 1 ：The given expression is $\sqrt{x}\cdot \sqrt[7]{x}\cdot \sqrt[7]{x}$. We know that $\sqrt{x}$ is equivalent to $x^{\frac{1}{2}}$ and $\sqrt[7]{x}$ is equivalent to $x^{\frac{1}{7}}$. So, the expression can be rewritten as $x^{\frac{1}{2}}\cdot x^{\frac{1}{7}}\cdot x^{\frac{1}{7}}$.

Step 2 ：When multiplying expressions with the same base, we add the exponents. So, the simplified form of the expression is $x^{\frac{1}{2}+\frac{1}{7}+\frac{1}{7}}$.

Step 3 ：The simplified form of the expression is $x^{0.785714285714286}$. However, this is not in the form of a fraction. We need to convert this decimal to a fraction to match the answer choices.

Step 4 ：The decimal 0.785714285714286 can be converted to the fraction $\frac{11}{14}$.

Step 5 ：$\boxed{{\displaystyle x^{\frac{11}{14}}}}$ is the simplified form of the expression $\sqrt{x}\cdot \sqrt[7]{x}\cdot \sqrt[7]{x}$. However, this option is not given in the answer choices. There might be a mistake in the question or the answer choices.