Question

Convert the following expression to simplify faction or integer. If it is not a real number, enter None

Answer 1

Given an expression:

`81^{-(1)/(4)}`

We have to simplify the given expression.

We know that:

`x^(-a)=(1)/(x^a)`

So,

`81^{-(1)/(4)}=\frac{1}{81^{(1)/(4)}}`

Let:

`\begin{gathered} x=\frac{1}{81^{(1)/(4)}} \\ \Rightarrow x^4=(\frac{1}{81^{(1)/(4)}})^4 \\ \Rightarrow x^4=(1)/(81) \\ \Rightarrow x^4=((1)/(3))^4 \\ \Rightarrow x=(1)/(3) \end{gathered}`

Thus, the answer is 1/3.