Simplifying Algebraic Expressions: 5x^2y(2x^4y^-3)
In algebra, simplifying expressions is an essential skill to master. In this article, we will explore how to simplify the expression 5x^2y(2x^4y^-3).
Step 1: Understand the Expression
The given expression is 5x^2y(2x^4y^-3). To simplify this expression, we need to follow the order of operations (PEMDAS) and combine like terms.
Step 2: Multiply the Coefficients
First, we multiply the coefficients of the two terms: 5 and 2. This gives us:
5 × 2 = 10
Step 3: Multiply the Variables
Next, we multiply the variables x and y. We need to multiply the exponents of x and y separately.
x^2 × x^4 = x^(2+4) = x^6
y × y^-3 = y^(1-3) = y^-2
Step 4: Combine the Results
Now, we combine the results of steps 2 and 3:
10x^6y^-2
Simplified Expression
The simplified expression is 10x^6y^-2.
Conclusion
Simplifying algebraic expressions requires attention to detail and a solid understanding of the rules of exponents. By following the correct order of operations and combining like terms, we can simplify complex expressions like 5x^2y(2x^4y^-3) into a more manageable form.
