Given an expression:
[tex]81^{-\frac{1}{4}}[/tex]
We have to simplify the given expression.
We know that:
[tex]x^{-a}=\frac{1}{x^a}[/tex]
So,
[tex]81^{-\frac{1}{4}}=\frac{1}{81^{\frac{1}{4}}}[/tex]
Let:
[tex]\begin{gathered} x=\frac{1}{81^{\frac{1}{4}}} \\ \Rightarrow x^4=(\frac{1}{81^{\frac{1}{4}}})^4 \\ \Rightarrow x^4=\frac{1}{81} \\ \Rightarrow x^4=(\frac{1}{3})^4 \\ \Rightarrow x=\frac{1}{3} \end{gathered}[/tex]
Thus, the answer is 1/3.
