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.
1 answer