Given an expression:
[tex](-81)^{\frac{1}{4}}[/tex]
We have to simplify the expression, if it does not result in a real number then the answer is NONE.
Let:
[tex]x=(-81)^{\frac{1}{4}}[/tex]
Then,
[tex]\begin{gathered} x=(-81)^{\frac{1}{4}} \\ \Rightarrow x^4=((-81)^{\frac{1}{4}})^4 \\ \Rightarrow x^4=-81 \end{gathered}[/tex]
There is no real number whose power 4 is a negative number.
Thus, the answer is not a real number. The answer is NONE.
