Write with Rational (Fractional) Exponents eighth root of x^6

$\sqrt[8]{x^{6}}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[8]{x^{6}}$ as $x^{\frac{6}{8}}$ .

$x^{\frac{6}{8}}$

Cancel the common factor of $6$ and $8$ .

Factor $2$ out of $6$ .

$x^{\frac{2 (3)}{8}}$

Cancel the common factors.

Factor $2$ out of $8$ .

$x^{\frac{2 \cdot 3}{2 \cdot 4}}$

Cancel the common factor.

$x^{\frac{2 \cdot 3}{2 \cdot 4}}$

Rewrite the expression.

$x^{\frac{3}{4}}$