If [tex]n>1[/tex], we write [tex]x^{1/n}=\sqrt[n]x[/tex]. So
[tex]\left(\dfrac1{81}\right)^{1/4}=\sqrt[4]{\dfrac1{81}}[/tex]
We can simplify this further by using properties of square roots:
[tex]\sqrt{\dfrac ab}=\dfrac{\sqrt a}{\sqrt b}\implies\sqrt[4]{\dfrac1{81}}=\dfrac{\sqrt[4]1}{\sqrt[4]{81}}=\dfrac1{\sqrt[4]{81}}[/tex]
Next, [tex]81=9^2=(3^2)^2=3^4[/tex], and so [tex]\sqrt[4]{81}=\sqrt[4]{3^4}=3[/tex], so
[tex]\left(\dfrac1{81}\right)^{1/4}=\dfrac13[/tex]
