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The expression you provided is:

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

To simplify this, we can use the property of exponents:

\[
a^m \times a^n = a^{m+n}
\]

Applying this property, we have:

\[
81^{\frac{1}{4}} \times 81^{\frac{1}{4}} = 81^{\frac{1}{4} + \frac{1}{4}} = 81^{\frac{2}{4}} = 81^{\frac{1}{2}}
\]

Now, \( 81^{\frac{1}{2}} \) is the square root of 81:

\[
81^{\frac{1}{2}} = \sqrt{81} = 9
\]

Thus, the simplified value of the expression is \( 9 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the general rule for multiplying powers with the same base?
2. How can you simplify the expression \( a^{\frac{m}{n}} \)?
3. What is the cube root of 81 and how does it compare to the fourth root?
4. How do you solve expressions with different fractional exponents?
5. How can you simplify expressions involving both roots and powers?

**Tip:** When multiplying exponents with the same base, always add the exponents.

Learn how to simplify the expression 81^(1/4) * 81^(1/4) using the properties of exponents. The problem covers exponent addition and simplifies to the square root of 81. Suitable for high school students in Grades 9-12.

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