## Simplifying the Expression: (6x^8y^2/12x^3y^7)^2

This article will walk you through the process of simplifying the expression (6x^8y^2/12x^3y^7)^2. We'll use the rules of exponents to achieve a simplified form.

### 1. Simplifying the Fraction Inside the Parentheses

Before we square the entire expression, let's simplify the fraction inside the parentheses:

**Divide the coefficients:**6/12 simplifies to 1/2.**Subtract the exponents of x:**x^8 / x^3 = x^(8-3) = x^5.**Subtract the exponents of y:**y^2 / y^7 = y^(2-7) = y^-5.

This leaves us with (1/2 * x^5 * y^-5).

### 2. Squaring the Simplified Expression

Now, we square the entire simplified expression:

**Square the coefficient:**(1/2)^2 = 1/4.**Square the x term:**(x^5)^2 = x^(5*2) = x^10.**Square the y term:**(y^-5)^2 = y^(-5*2) = y^-10.

Combining these, we get (1/4 * x^10 * y^-10).

### 3. Rewriting with Positive Exponent

Finally, we can express the result with a positive exponent for y:

**Remember:**y^-10 = 1/y^10.

This gives us the final simplified form: **(x^10) / (4y^10)**.

### Conclusion

Therefore, the simplified form of (6x^8y^2/12x^3y^7)^2 is **(x^10) / (4y^10)**. By applying the rules of exponents and simplifying step by step, we arrive at this concise and clear representation.