Simplify the expression to a single power of $x$. \[ \left(\frac{x^{\frac{3}{4}}}{x^{\frac{1}{3}}}\right)^{\frac{2}{3}} \]

Step 1 ：Apply the property of exponents: \(\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}\)

Step 2 ：Apply the property to the given expression: \(\left(\frac{x^{\frac{3}{4}}}{x^{\frac{1}{3}}}\right)^{\frac{2}{3}} = \frac{(x^{\frac{3}{4}})^{\frac{2}{3}}}{(x^{\frac{1}{3}})^{\frac{2}{3}}}\)

Step 3 ：Simplify the exponents by multiplying the numerator and denominator by the exponent: \(\frac{x^{\frac{3}{4} \cdot \frac{2}{3}}}{x^{\frac{1}{3} \cdot \frac{2}{3}}} = \frac{x^{\frac{1}{2}}}{x^{\frac{2}{9}}}\)

Step 4 ：Divide the exponents by subtracting them: \(x^{\frac{1}{2} - \frac{2}{9}} = x^{\frac{9}{18} - \frac{4}{18}} = x^{\frac{5}{18}}\)

Step 5 ：The simplified expression is \(\boxed{x^{\frac{5}{18}}}\)