Question

simplify.
\sqrt4{\frac{1}{81}}
be sure to write your answer in lowest terms.

Explanation:

Step1: Recall nth root properties

The nth root of a fraction $\sqrt[n]{\frac{a}{b}}$ can be written as $\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$. So, $\sqrt[4]{\frac{1}{81}}=\frac{\sqrt[4]{1}}{\sqrt[4]{81}}$.

Step2: Simplify numerator and denominator

We know that $\sqrt[4]{1} = 1$ (since $1^4 = 1$) and we need to find the fourth root of 81. We know that $3^4=81$ (because $3\times3\times3\times3 = 81$), so $\sqrt[4]{81}=3$.

Step3: Divide the results

Now, we have $\frac{\sqrt[4]{1}}{\sqrt[4]{81}}=\frac{1}{3}$.

Answer:

$\frac{1}{3}$