https://file.aiquickdraw.com/mathbot/file/1727040012725sscfezei.jpg

The expression in the image is:

\[
\left( \frac{81}{100} \right)^{-\frac{1}{2}}
\]

Let's solve it step by step.

### Step 1: Simplify the expression
The negative exponent can be rewritten as a reciprocal:

\[
\left( \frac{81}{100} \right)^{-\frac{1}{2}} = \frac{1}{\left( \frac{81}{100} \right)^{\frac{1}{2}}}
\]

### Step 2: Apply the square root
Raising a fraction to the power of \( \frac{1}{2} \) means taking the square root of both the numerator and the denominator:

\[
\sqrt{\frac{81}{100}} = \frac{\sqrt{81}}{\sqrt{100}} = \frac{9}{10}
\]

### Step 3: Substitute back into the expression
Now substitute \( \frac{9}{10} \) into the reciprocal expression:

\[
\frac{1}{\frac{9}{10}} = \frac{10}{9}
\]

Thus, the value of the given expression is:

\[
\boxed{\frac{10}{9}}
\]

Would you like further details or any clarifications?

Here are 5 related questions:
1. What is the rule for dealing with negative exponents?
2. How do you simplify expressions involving square roots of fractions?
3. What is the general process for solving rational exponent equations?
4. Can you apply the same steps to a similar problem like \( \left( \frac{16}{25} \right)^{-\frac{1}{2}} \)?
5. How would you handle a different power, like \( \left( \frac{81}{100} \right)^{-\frac{3}{2}} \)?

**Tip:** Remember that negative exponents represent reciprocal values, which is an important tool in simplifying complex expressions.

Learn how to simplify the expression (81/100)^(-1/2) using exponent and square root rules. This step-by-step solution involves applying negative exponent laws, taking square roots of fractions, and finding the reciprocal. Ideal for students in Grades 7-9.

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