To simplify \( \left( \frac{8x^4}{y} \right)^{-2} \), follow these steps:

### Step 1: Apply the Negative Exponent Rule
The negative exponent rule states that \( a^{-n} = \frac{1}{a^n} \). So applying this to the expression:

\[
\left( \frac{8x^4}{y} \right)^{-2} = \frac{1}{\left( \frac{8x^4}{y} \right)^2}
\]

### Step 2: Apply the Exponent to Both Numerator and Denominator
Now, square both the numerator and the denominator:

\[
\frac{1}{\left( \frac{8x^4}{y} \right)^2} = \frac{1}{\frac{(8x^4)^2}{y^2}} = \frac{y^2}{(8x^4)^2}
\]

### Step 3: Square the Terms in the Numerator and Denominator
- \( (8x^4)^2 = 8^2 \cdot (x^4)^2 = 64x^8 \)
  
So the expression becomes:

\[
\frac{y^2}{64x^8}
\]

### Final Simplified Expression:
\[
\frac{y^2}{64x^8}
\]

Would you like to explore this more, or ask for more examples?

Here are some related questions:
1. How do you simplify expressions with negative exponents?
2. What are some rules for applying exponents to fractions?
3. How do you square terms involving both constants and variables?
4. How do negative exponents affect fractions in more complex expressions?
5. Can you explain how to simplify \( (a^m/b^n)^{-p} \)?

**Tip:** When raising fractions to a power, apply the exponent to both the numerator and the denominator separately.

Learn how to simplify the expression (8x^4/y)^-2 with detailed step-by-step instructions. This problem involves applying the negative exponent rule and handling fractional exponents. Suitable for Grades 7-9 students studying exponents and algebra.

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