https://file.aiquickdraw.com/mathbot/file/1725486216876pseznz4s.jpg

The image contains a mathematical expression that needs to be simplified. The expression is:

\[
\left(\frac{x^5}{y^8}\right)^{-2}
\]

To simplify the expression with positive exponents, follow these steps:

### Step 1: Apply the negative exponent rule
The rule for a negative exponent is that \(a^{-n} = \frac{1}{a^n}\). So, we first apply this rule:

\[
\left(\frac{x^5}{y^8}\right)^{-2} = \left(\frac{y^8}{x^5}\right)^2
\]

### Step 2: Apply the power of a quotient rule
Next, we apply the exponent to both the numerator and the denominator. The power of a quotient rule is \(\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}\):

\[
\left(\frac{y^8}{x^5}\right)^2 = \frac{(y^8)^2}{(x^5)^2}
\]

### Step 3: Simplify each term
Now, simplify each term by applying the power to the exponents:

\[
\frac{y^{16}}{x^{10}}
\]

### Final Answer
The simplified expression with positive exponents is:

\[
\frac{y^{16}}{x^{10}}
\]

---

Would you like more details on any of these steps? Here are some related questions to deepen your understanding:

1. How do you simplify expressions with multiple negative exponents?
2. What is the general rule for dealing with exponents in a fraction?
3. How do you simplify an expression with both a negative exponent and a power?
4. Can you apply these steps to a different example, such as \(\left(\frac{a^3}{b^2}\right)^{-4}\)?
5. What happens if there are variables in both the numerator and the denominator with negative exponents?

**Tip:** Always remember to apply the negative exponent rule first before simplifying the expression further.

Simplify the given expression. Write your answer with positive exponents.

Learn how to simplify the expression (x^5/y^8)^(-2) and write your answer with positive exponents. This problem involves key algebraic concepts such as the negative exponent rule and the power of a quotient rule. Suitable for students in Grades 8-10.

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