https://file.aiquickdraw.com/mathbot/file/17260983033611rws145b.jpg

The expression in the image is:

\[
\left( \frac{2xy}{\frac{3}{5}} \right)^{-1}
\]

Let's simplify and solve this step by step:

### Step 1: Simplify the fraction inside the parentheses
The fraction \(\frac{3}{5}\) appears in the denominator. Therefore, the entire expression becomes:

\[
\frac{2xy}{\frac{3}{5}} = 2xy \times \frac{5}{3} = \frac{10xy}{3}
\]

### Step 2: Apply the exponent \(-1\)
When we apply the \(-1\) exponent, we take the reciprocal of the fraction:

\[
\left( \frac{10xy}{3} \right)^{-1} = \frac{3}{10xy}
\]

Thus, the simplified expression is:

\[
\frac{3}{10xy}
\]

Let me know if you need further details or explanations on any step.

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Here are five related questions:
1. What happens when you apply an exponent of \(-2\) instead of \(-1\)?
2. How would you solve this expression if the exponent were a fraction, such as \(\frac{1}{2}\)?
3. What if the variable \(y\) equals zero in this expression? How would the expression change?
4. How does multiplying by negative exponents affect the sign of the final answer?
5. What if the fraction inside had been \(\frac{5}{3}\) instead of \(\frac{3}{5}\)?

**Tip**: Always simplify the expression inside parentheses before applying exponents, especially negative ones!

Learn how to simplify an algebraic expression involving a fraction and a negative exponent: (2xy / (3/5))^(-1). This problem covers core algebra concepts such as negative exponents, fraction simplification, and reciprocal application. Suitable for Grades 8-10.

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