Question

Solve for
\[n\].
\[\left(2^4\right)^{2}=2^n\]
\[n=\]

Answer 1

To solve for \( n \) in the equation

\[
\left(2^4\right)^{2} = 2^n,
\]

we can simplify the left-hand side using the property of exponents \( (a^m)^n = a^{m \cdot n} \).

Applying this property, we have:

\[
\left(2^4\right)^{2} = 2^{4 \cdot 2}.
\]

Calculating \( 4 \cdot 2 \) gives:

\[
4 \cdot 2 = 8,
\]

so we can rewrite the left-hand side as:

\[
2^{8}.
\]

Now our equation looks like:

\[
2^{8} = 2^n.
\]

Since the bases are the same, we can set the exponents equal to each other:

\[
8 = n.
\]

Thus, we find that

\[
n = 8.
\]

The final answer is

\[
\boxed{8}.
\]