Answer :

To solve the expression [tex]\(\left(\sqrt{2^4}\right)^{-1}\)[/tex] step-by-step, let's break it down into the following parts:

1. Calculate the exponentiation [tex]\(2^4\)[/tex]:
[tex]\[ 2^4 = 2 \times 2 \times 2 \times 2 = 16 \][/tex]

2. Take the square root of the result:
[tex]\[ \sqrt{16} = 4 \][/tex]

3. Find the inverse of the square root:
[tex]\[ \left(4\right)^{-1} = \frac{1}{4} = 0.25 \][/tex]

Thus, the value of the expression [tex]\(\left(\sqrt{2^4}\right)^{-1}\)[/tex] is:

[tex]\[ \left(\sqrt{2^4}\right)^{-1} = 0.25 \][/tex]

In summary:
- The exponentiation [tex]\(2^4\)[/tex] equals 16.
- The square root of 16 is 4.
- The inverse of 4 is 0.25.

Therefore, the final answer is [tex]\(0.25\)[/tex].