If I understood coorectly, you're looking for the fourth root of 81. This exercise can be solved by remembering that extracting the fourth root of a number is the same as raising that number to the power of 1/4.
We also need the prime factorization of 81, which is
[tex] 81 = 9 \times 9 = 3^2 \times 3^2 = 3^4 [/tex]
So, the fourth root of 81 is 81 raised to the power of 1/4, which means
[tex] \sqrt[4]{81} = \sqrt[4]{3^4} = (3^4)^{\frac{1}{4}} [/tex]
Now, use the property of exponents [tex] (a^b)^c = a^{bc} [/tex] to convert the expression into
[tex] (3^4)^{\frac{1}{4}} = 3^{4\cdot \frac{1}{4}} = 3^1 = 3[/tex]
[tex] 81|3\\27|3\\.\ 9|3\\.\ 3|3\\.\ 1|\\\\81=\underbrace{3\cdot3\cdot3\cdot3}_{4}=3^4\\\\\sqrt[4]{81}=\sqrt[4]{3^4}=3\\\\Used:\\\sqrt[n]{a^n}=a [/tex]
