To solve the equation \((16^x)^6 = 16^{18}\), we can use the properties of exponents.
First, apply the power of a power property, which states that \((a^m)^n = a^{m \cdot n}\):
\[ (16^x)^6 = 16^{x \cdot 6} = 16^{6x} \]
Now, we can rewrite the equation as:
\[ 16^{6x} = 16^{18} \]
Since the bases are the same (both are \(16\)), we can equate the exponents:
\[ 6x = 18 \]
Next, solve for \(x\) by dividing both sides by \(6\):
\[ x = \frac{18}{6} = 3 \]
Thus, the exponent \(x\) that makes the two expressions equivalent is:
\[ \boxed{3} \]