Final answer:
The expression (6x³y³)/(9xµy) simplifies to (2/3)x^(-2)y^2. To check the answer, evaluate both the original and simplified expressions using specific values for x and y to confirm they yield the same result.
Step-by-step explanation:
The question involves simplifying the algebraic expression (6x³y³)/(9xµy) and then checking the simplification by evaluating it at an appropriate value. To simplify this expression, we need to divide the coefficients and subtract the exponents of like terms.
Simplification:
- Divide the coefficients: 6/9 simplifies to 2/3.
- Subtract the exponents of x: x³ divided by xµ is x^(3-5), which simplifies to x^(-2).
- Subtract the exponents of y: y³ divided by y is y^(3-1), which simplifies to y^2.
The simplified expression is (2/3)x^(-2)y^2.
To check the answer, select an appropriate value for x and y (preferably integers to keep calculation simple), substitute them into the original and simplified expressions to see if they yield the same result.
Examples:
- Choose x=1 and y=1. Then, the original expression equals (6*1³*1³)/(9*1µ*1) = 6/9 = 2/3, and the simplified expression equals (2/3)*1^(-2)*1^2 = 2/3, which confirms the simplification is correct.
- Or, choose x=2 and y=3. Then, the original expression equals (6*2³*3³)/(9*2µ*3) which should equal the simplified expression when calculated.
After calculating, ensure that the results make sense, which means checking that the numerical value is consistent with mathematical rules and that physical units (if any) are appropriate.