%5E2(x%2B4)%5E3-simplify.jpeg "(x+4)^2(x+4)^3 Simplify")
Simplifying (x+4)^2(x+4)^3
In mathematics, simplifying expressions is crucial for understanding their meaning and manipulating them efficiently. Let's explore how to simplify the expression (x+4)^2(x+4)^3.
Understanding the Properties
The key to simplifying this expression lies in understanding the properties of exponents. Recall that:
- x^m * x^n = x^(m+n)
This property states that when multiplying powers with the same base, we can add the exponents.
Applying the Property
- Identify the base: In this case, the base is (x+4).
- Add the exponents: We have (x+4)^2 * (x+4)^3. The exponents are 2 and 3. Adding them gives us 2 + 3 = 5.
The Simplified Expression
Therefore, the simplified expression is (x+4)^5.
Conclusion
By understanding and applying the properties of exponents, we can simplify expressions like (x+4)^2(x+4)^3 to a more manageable form. This simplification makes it easier to work with the expression in further calculations or analysis.