%5E2(2x%5E4y%5E3)%2F6x%5E8y.jpeg "(3xy)^2(2x^4y^3)/6x^8y")
Simplifying Algebraic Expressions: (3xy)^2(2x^4y^3)/6x^8y
This article will guide you through simplifying the algebraic expression: (3xy)^2(2x^4y^3)/6x^8y. We will break down the process step by step, ensuring you understand each stage.
Step 1: Expanding the Expression
Begin by expanding the expression using the rules of exponents:
- (3xy)^2 = 3^2 * x^2 * y^2 = 9x^2y^2
Now, our expression becomes: (9x^2y^2)(2x^4y^3)/6x^8y
Step 2: Multiplying the Numerator
Next, multiply the terms in the numerator:
- (9x^2y^2)(2x^4y^3) = 18x^(2+4)y^(2+3) = 18x^6y^5
The expression now reads: 18x^6y^5 / 6x^8y
Step 3: Simplifying the Expression
To simplify, divide the coefficients and subtract the exponents of the same variables in the numerator and denominator:
- 18 / 6 = 3
- x^(6-8) = x^(-2)
- y^(5-1) = y^4
Therefore, the simplified expression becomes: 3x^(-2)y^4
Step 4: Expressing the Result with Positive Exponents
Finally, we can express the result using positive exponents by moving the term with the negative exponent to the denominator:
3y^4/x^2
Conclusion
The simplified form of the expression (3xy)^2(2x^4y^3)/6x^8y is 3y^4/x^2. By following the steps outlined above, you can confidently simplify complex algebraic expressions. Remember, understanding the rules of exponents and applying them correctly is crucial for achieving accurate results.