%5E2.jpeg "(6x^8y^2/12x^3y^7)^2")
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.