Question

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

8
8
4
4
84
84
no solution

Answer 1

To solve the equation \(2x^{32} = 16\), we can start by isolating \(x^{32}\).

1. Divide both sides by 2:
\[
x^{32} = \frac{16}{2}
\]
\[
x^{32} = 8
\]

2. Now we need to solve for \(x\). Take the 32nd root of both sides, which can be expressed using a rational exponent:
\[
x = 8^{\frac{1}{32}}
\]

3. We know that \(8\) can be expressed as \(2^3\):
\[
x = (2^3)^{\frac{1}{32}} = 2^{\frac{3}{32}}
\]

Now we will evaluate \(x\) to check if it matches any of the provided options:

- The options presented are: 8, 4, 84, and no solution.

Since \(2^{\frac{3}{32}}\) is a very small number (as \(3/32\) is less than 1), it will not match any of the whole numbers given in the options.

Thus, the correct choice from the options is:

**no solution**.