We will have the following:
![\sqrt[]{(16)/(81)}=\frac{\sqrt[]{16}}{\sqrt[]{81}}=(4)/(9)](https://img.qammunity.org/2023/formulas/mathematics/high-school/h8y4b3h0xin71s9o6613bwn5f6cd1pxj7y.png)
So, the expression in its simplest form is 4/9.
***Explanation***
First we are given the expression:
![\sqrt[]{(16)/(81)}](https://img.qammunity.org/2023/formulas/mathematics/high-school/w33uzhhha4mz1yuy872naazk62vrrnover.png)
From the properties of roots, we will have that if a root contains a fraction, then we can rewrite the expression applying the root to the numerator and denominator [Separately], this is:
![\sqrt[]{(16)/(81)}=\frac{\sqrt[]{16}}{\sqrt[]{81}}](https://img.qammunity.org/2023/formulas/mathematics/high-school/416fn8hr0zhfhjjok0fvsmyxg2xa6jndu2.png)
Since, these expressions are equivalent, then we solve for each one, that is:
![\begin{cases}\sqrt[]{16}=4 \\ \& \\ \sqrt[]{81}=9\end{cases}](https://img.qammunity.org/2023/formulas/mathematics/high-school/l1daxehjnqpz18m20o1bvjgxnr85tisoke.png)
Then, we simply replace in the fraction form:
![\sqrt[]{(16)/(81)}=(4)/(9)](https://img.qammunity.org/2023/formulas/mathematics/high-school/ohp9n8l9o2gw8pmmwnd9cmdz3cybs2yvjl.png)