To solve the equation \((16x)^6 = (16^{18})\), we will start by analyzing both sides.
The left side, \((16x)^6\), can be rewritten using the distributive property of exponents as:
\[ (16^6)(x^6) \]
Now we need to compare this with the right side, which is \(16^{18}\).
Setting the two parts equal, we have:
\[ 16^6 \cdot x^6 = 16^{18} \]
Now we can divide both sides by \(16^6\):
\[ x^6 = \frac{16^{18}}{16^6} = 16^{18-6} = 16^{12} \]
Next, we can take the sixth root of both sides:
\[ x = (16^{12})^{1/6} = 16^{12/6} = 16^2 \]
Since \(16 = 2^4\), we can express \(16^2\) as:
\[ 16^2 = (2^4)^2 = 2^{4 \cdot 2} = 2^8 \]
Thus, we find:
\[ x = 2^8 \]
This means that \(x\) is equivalent to \(2^8\). However, the original question asked for the exponent that would make the two expressions equivalent, not necessarily the value of \(x\).
If we were asked to find a value \(n\) such that \((16x)^n = 16^{18}\), and if we maintain that equality leads from \(x=16^{2}\), then setting \(n=6\) indeed holds for both expressions as shown previously.
In summary, to make the two expressions \((16x)^6\) and \(16^{18}\) equivalent, the exponent needed from this setup is:
\[ n = 6 \]
If you meant the exponent from setting \(x = 16^{2}\) wherein exponenting from an ozone factor could be taken on \(x^{n}\) through that equality relationship, please clarify else \(6\) consistently makes both sides valid equivalently.
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