https://file.aiquickdraw.com/mathbot/file/1726797965932rxjiv6vp.jpg

The expression given in the image is:

\[
\frac{1}{81^{1/4}}
\]

This can be simplified as follows:

1. Recognize that \(81^{1/4}\) means the 4th root of 81.
2. Since \(81 = 3^4\), we can rewrite \(81^{1/4} = (3^4)^{1/4} = 3\).

Therefore, the expression simplifies to:

\[
\frac{1}{3}
\]

So, the value of the expression is \(\frac{1}{3}\) or approximately 0.333.

Would you like more details or have any further questions?

Here are some related questions for deeper understanding:
1. What is the general method for simplifying fractional exponents?
2. How do you calculate roots of larger numbers efficiently?
3. What are the properties of exponents when dealing with roots?
4. How would the solution change if it were \(81^{1/3}\) instead of \(81^{1/4}\)?
5. How can you express \(\frac{1}{81^{1/4}}\) as a decimal?

**Tip**: When simplifying expressions with roots, always check if the base can be expressed as a power of smaller numbers to make calculations easier.

Learn how to simplify the expression 1 / 81^(1/4) using exponent and root properties. This step-by-step guide explains how to find the fourth root of 81 and provides a detailed solution. Ideal for students in Grades 8-10.

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