(2x%5E-3y)%5E-1.jpeg "(12x^3-16x^2y+3xy^2+9y^2)(2x^-3y)^-1")
Simplifying Algebraic Expressions: A Step-by-Step Guide
In this article, we will explore the simplification of the algebraic expression (12x^3 - 16x^2y + 3xy^2 + 9y^2)(2x^-3y)^-1. We will break down the expression into manageable parts and apply mathematical operations to simplify it.
Step 1: Simplify the Expression Inside the Parentheses
Let's start by simplifying the expression inside the parentheses:
12x^3 - 16x^2y + 3xy^2 + 9y^2
This expression is a polynomial, which can be simplified by combining like terms. However, in this case, there are no like terms to combine. So, we'll leave it as is.
Step 2: Simplify the Exponent of the Second Factor
Now, let's focus on the exponent of the second factor (2x^-3y)^-1. When we raise an expression to a negative power, it is equivalent to raising the reciprocal of the expression to a positive power. Therefore, we can rewrite the exponent as:
(2x^-3y)^-1 = (1 / (2x^-3y))
Step 3: Simplify the Entire Expression
Now that we have simplified the exponent, we can rewrite the entire expression as:
(12x^3 - 16x^2y + 3xy^2 + 9y^2) * (1 / (2x^-3y))
To simplify this expression, we need to multiply the two factors. We'll start by rewriting the first factor with a common denominator:
12x^3 - 16x^2y + 3xy^2 + 9y^2 = (12x^3 / x^3) - (16x^2y / x^3) + (3xy^2 / x^3) + (9y^2 / x^3)
Now, we can multiply the two factors:
((12x^3 / x^3) - (16x^2y / x^3) + (3xy^2 / x^3) + (9y^2 / x^3)) * (1 / (2x^-3y))
Step 4: Simplify the Final Expression
After multiplying the two factors, we get:
(6x^6 - 8x^3y + 3xy^2 + 9y^2) / (2x^-3y)
This is the simplified form of the original expression.
Conclusion
In this article, we have successfully simplified the algebraic expression (12x^3 - 16x^2y + 3xy^2 + 9y^2)(2x^-3y)^-1 by breaking it down into manageable parts and applying mathematical operations. The final simplified expression is (6x^6 - 8x^3y + 3xy^2 + 9y^2) / (2x^-3y).
