%5E3(4xy%5E4)%5E2%2F8x%5E7y%5E12.jpeg "(2x^5y^3)^3(4xy^4)^2/8x^7y^12")
Simplifying Algebraic Expressions: A Step-by-Step Guide
This article will guide you through simplifying the algebraic expression: (2x^5y^3)^3(4xy^4)^2/8x^7y^12
Let's break down the process step by step:
1. Expanding the Parentheses
First, we need to apply the power rule for exponents: (a^m)^n = a^(m*n) to expand the parentheses.
- (2x^5y^3)^3: This becomes 2^3 * (x^5)^3 * (y^3)^3 = 8x^15y^9
- (4xy^4)^2: This becomes 4^2 * (x)^2 * (y^4)^2 = 16x^2y^8
Now our expression looks like this: (8x^15y^9)(16x^2y^8)/8x^7y^12
2. Combining Like Terms
Next, we multiply the coefficients and add the exponents of the variables with the same base.
- 8 * 16 / 8 = 16
- x^15 * x^2 = x^17
- y^9 * y^8 = y^17
This gives us: 16x^17y^17 / 8x^7y^12
3. Simplifying the Expression
Finally, we divide the coefficients and subtract the exponents of the variables with the same base.
- 16 / 8 = 2
- x^17 / x^7 = x^10
- y^17 / y^12 = y^5
Therefore, the simplified expression is 2x^10y^5.
Summary
By following these steps, we have successfully simplified the complex algebraic expression. The key takeaways are:
- Apply the power rule for exponents to expand parentheses.
- Combine like terms by multiplying coefficients and adding exponents of the same base.
- Simplify the expression by dividing coefficients and subtracting exponents of the same base.
Remember, practice makes perfect! By working through similar problems, you can build confidence and proficiency in simplifying algebraic expressions.