To solve the equation \( 2x^{32} = 16 \), we can first express 16 in terms of a power of 2:
\[ 16 = 2^4 \]
This allows us to rewrite the equation as:
\[ 2x^{32} = 2^4 \]
Now, we can divide both sides by 2 (assuming \( x^{32} \neq 0 \)):
\[ x^{32} = 2^3 \]
This simplifies to:
\[ x^{32} = 8 \]
Now, to solve for \( x \), we take the 32nd root of both sides:
\[ x = 8^{\frac{1}{32}} \]
Next, since \( 8 = 2^3 \), we can rewrite this as:
\[ x = (2^3)^{\frac{1}{32}} = 2^{\frac{3}{32}} \]
Thus, the solution can be expressed as:
\[ x = 2^{\frac{3}{32}} \]
This result does not match any of the given responses exactly, implying that there is no solution among the provided options.
Therefore, the correct response is:
no solution
1 answer