To solve the equation \((3^3)^x = 3^{24}\), we can use the property of exponents which states that \((a^m)^n = a^{m \cdot n}\).
Applying this property:
\[ (3^3)^x = 3^{3x} \]
So, the equation becomes:
\[ 3^{3x} = 3^{24} \]
Since the bases are the same, we can set the exponents equal to each other:
\[ 3x = 24 \]
Now, solve for \(x\):
\[ x = \frac{24}{3} = 8 \]
Therefore, the exponent that makes the two expressions equivalent is:
8.