Simplify: \((\frac{16}{81})^{\frac{1}{4}}\)

To simplify \((\frac{16}{81})^{\frac{1}{4}}\), we need to take the fourth root of \(\frac{16}{81}\). The fourth root of a number is the number that, when multiplied by itself four times, gives that number. So, to find the fourth root of \(\frac{16}{81}\), we need to find a number that, when multiplied by itself four times, gives \(\frac{16}{81}\). We can rewrite \(\frac{16}{81}\) as \((\frac{2}{3})^4\), since \(2^4=16\) and \(3^4=81\). Therefore, \((\frac{16}{81})^{\frac{1}{4}} = ((\frac{2}{3})^4)^{\frac{1}{4}} = \frac{2}{3}\), which is.