The expression is:

\[
25^{-\frac{1}{2}} \times 84^{\frac{3}{4}}
\]

Let's break it down step by step:

### 1. Simplify \( 25^{-\frac{1}{2}} \)
The expression \( 25^{-\frac{1}{2}} \) is the reciprocal of the square root of 25. Since \( 25 = 5^2 \), we have:

\[
25^{-\frac{1}{2}} = \frac{1}{\sqrt{25}} = \frac{1}{5}
\]

### 2. Simplify \( 84^{\frac{3}{4}} \)
The expression \( 84^{\frac{3}{4}} \) means taking the 4th root of 84, then cubing it. However, since \( 84 \) does not have a perfect 4th root, we'll leave the result in this form for now. It can be expressed as:

\[
84^{\frac{3}{4}} = \sqrt[4]{84^3}
\]

### 3. Multiply the simplified expressions
Now we multiply the two expressions:

\[
\frac{1}{5} \times 84^{\frac{3}{4}} = \frac{84^{\frac{3}{4}}}{5}
\]

Thus, the simplified result is:

\[
\frac{84^{\frac{3}{4}}}{5}
\]

This is the simplified form of the expression.

Do you need more details or any further clarifications?

Here are 5 related questions for practice:
1. What is \( 16^{-\frac{1}{2}} \times 32^{\frac{1}{5}} \)?
2. How do you evaluate \( 36^{-\frac{1}{2}} \times 49^{\frac{3}{2}} \)?
3. What is the simplified result of \( 64^{\frac{1}{6}} \times 27^{\frac{2}{3}} \)?
4. Can you find the value of \( 100^{\frac{1}{4}} \times 25^{-\frac{3}{2}} \)?
5. How do you simplify \( 8^{\frac{5}{6}} \times 125^{-\frac{2}{3}} \)?

**Tip**: For fractional exponents, the numerator represents a power, and the denominator represents a root.

Explore the step-by-step simplification of the expression 25^-1/2 x 84^3/4. This math problem focuses on fractional exponents and root concepts, breaking down each term clearly for students in Grades 9-11.

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