Solve the following equation with a rational exponent: 2x32=16.(1 point)

To solve the equation \( 2x^{32} = 16 \), we first isolate \( x^{32} \):

\[
x^{32} = \frac{16}{2}
\]
\[
x^{32} = 8
\]

Next, we can express 8 as a power of 2:

\[
8 = 2^3
\]

Now we have:

\[
x^{32} = 2^3
\]

To solve for \( x \), we can take the 32nd root of both sides or raise both sides to the power of \( \frac{1}{32} \):

\[
x = (2^3)^{\frac{1}{32}}
\]
\[
x = 2^{\frac{3}{32}}
\]

Now, let's compute \( 2^{\frac{3}{32}} \). Since it is not one of the integer values provided in the response options (4, 84, 8, or "no solution"), we conclude that the correct answer is not explicitly listed.

Thus, the answer is:

**no solution** (within the given options).