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

Question

Responses

16
16

8
8

32
32

512

Answer 1

To solve the equation \( x^{23} = 64 \), we can rewrite 64 as a power of 2. Since \( 64 = 2^6 \), we have:

\[ x^{23} = 2^6 \]

Next, we can solve for \( x \) by raising both sides to the power of \( \frac{1}{23} \):

\[ x = (2^6)^{\frac{1}{23}} = 2^{\frac{6}{23}} \]

Now, we need to check the provided options to find a numeric value that corresponds to \( 2^{\frac{6}{23}} \).

Let's evaluate the options given:

1. 16: \( 16 = 2^4 \) (which is not equal to \( 2^{\frac{6}{23}} \))
2. 8: \( 8 = 2^3 \) (which is not equal to \( 2^{\frac{6}{23}} \))
3. 32: \( 32 = 2^5 \) (which is not equal to \( 2^{\frac{6}{23}} \))
4. 512: \( 512 = 2^9 \) (which is not equal to \( 2^{\frac{6}{23}} \))

None of the provided options match \( 2^{\frac{6}{23}} \). Therefore, the solution to the original equation is not among the responses listed.

If you have other information or additional options, please let me know!