Solve the following equation with a rational exponent: x23=64 .(1 point)

To solve the equation \( x^{23} = 64 \), we need to isolate \( x \).

First, we can rewrite 64 with a base of 2:
\[
64 = 2^6
\]
Thus, our equation becomes:
\[
x^{23} = 2^6
\]

To isolate \( x \), we can take both sides of the equation to the power of \( \frac{1}{23} \):
\[
x = (2^6)^{\frac{1}{23}}
\]
This can be simplified using the property of exponents:
\[
x = 2^{\frac{6}{23}}
\]

Next, we need to determine which of the provided options is equivalent to \( 2^{\frac{6}{23}} \). We can evaluate the numerical values of the responses you provided:

- \( 32 = 2^5 \) (not a match)
- \( 8 = 2^3 \) (not a match)
- \( 16 = 2^4 \) (not a match)
- \( 512 = 2^9 \) (not a match)

None of the options are equal to \( 2^{\frac{6}{23}} \).

Thus, the correct answer isn't among the provided options. Please verify the options or the equation given.