To find the fourth root of 81, denoted as [tex]\( \sqrt[4]{81} \)[/tex], we need to determine a number that, when raised to the power of 4, equals 81.
Let's go through the process step-by-step:
1. Express 81 as a power of a smaller number, if possible:
[tex]\[
81 = 3^4
\][/tex]
2. We now need to find [tex]\( \sqrt[4]{81} \)[/tex], which translates to finding [tex]\( \sqrt[4]{3^4} \)[/tex].
3. According to the properties of exponents, [tex]\( \sqrt[4]{a^4} = a \)[/tex]. Therefore:
[tex]\[
\sqrt[4]{3^4} = 3
\][/tex]
Thus, the fourth root of 81 is indeed:
[tex]\[
\sqrt[4]{81} = 3
\][/tex]
So the answer to the question is [tex]\(3.0\)[/tex].
