To evaluate [tex]\((\sqrt[4]{81})^3\)[/tex], let's proceed step by step:
1. Find the fourth root of 81:
The fourth root of a number [tex]\( N \)[/tex] is the value that, when raised to the power of 4, gives [tex]\( N \)[/tex]. Hence, we're looking for a number [tex]\( x \)[/tex] such that [tex]\( x^4 = 81 \)[/tex].
[tex]\[
\sqrt[4]{81} = 3
\][/tex]
2. Raise the fourth root to the power of 3:
Now that we know the fourth root of 81 is 3, we need to raise this value to the power of 3:
[tex]\[
(\sqrt[4]{81})^3 = 3^3 = 27
\][/tex]
So the final value of [tex]\((\sqrt[4]{81})^3\)[/tex] is:
[tex]\[
27
\][/tex]
Therefore, [tex]\(\sqrt[4]{81} = 3\)[/tex] and [tex]\((\sqrt[4]{81})^3 = 27\)[/tex].
