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].
