Write with Rational (Fractional) Exponents fourth root of x^(2/3)

$\sqrt[4]{x^{\frac{2}{3}}}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{x^{\frac{2}{3}}}$ as $x^{\frac{\frac{2}{3}}{4}}$ .

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

Step 2

Multiply the numerator by the reciprocal of the denominator.

$x^{\frac{2}{3} \cdot \frac{1}{4}}$

Step 3

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$x^{\frac{2}{3} \cdot \frac{1}{2 (2)}}$

Cancel the common factor.

$x^{\frac{2}{3} \cdot \frac{1}{2 \cdot 2}}$

Rewrite the expression.

$x^{\frac{1}{3} \cdot \frac{1}{2}}$

Step 4

Multiply $\frac{1}{3}$ by $\frac{1}{2}$ .

$x^{\frac{1}{3 \cdot 2}}$

Step 5

Multiply $3$ by $2$ .

$x^{\frac{1}{6}}$