To solve for \( x \) in the expression \( \left(15^{\frac{1}{3}}\right)^{3} \), we can use the properties of exponents.
The property states that \( (a^m)^n = a^{mn} \). Applying this property here, we have:
\[ \left(15^{\frac{1}{3}}\right)^{3} = 15^{\frac{1}{3} \cdot 3} \]
Now we simplify the exponent:
\[ \frac{1}{3} \cdot 3 = 1 \]
Thus, we get:
\[ 15^{\frac{1}{3} \cdot 3} = 15^1 \]
This simplifies to:
\[ 15 \]
Therefore, the solution is:
\[ x = 15 \]