%5E2-times-(3a%5E2b).jpeg "(-4a^3b^2)^2 Times (3a^2b)")
Simplifying Expressions with Exponents
This article will guide you through the process of simplifying the expression (-4a^3b^2)^2 times (3a^2b).
Understanding the Rules
Before we begin, let's refresh our memory on some key rules of exponents:
- Product of Powers: When multiplying powers with the same base, you add the exponents. For example, x^m * x^n = x^(m+n)
- Power of a Product: To raise a product to a power, you raise each factor to that power. For example, (xy)^n = x^n * y^n
- Power of a Power: To raise a power to another power, you multiply the exponents. For example, (x^m)^n = x^(m*n)
Step-by-Step Simplification
- Simplify the first term: (-4a^3b^2)^2
- Apply the Power of a Product rule: (-4)^2 * (a^3)^2 * (b^2)^2
- Apply the Power of a Power rule: 16a^6b^4
- Write the full expression: 16a^6b^4 * 3a^2b
- Combine like terms: (16 * 3) * (a^6 * a^2) * (b^4 * b)
- Apply the Product of Powers rule: 48a^8b^5
Final Result
The simplified expression is 48a^8b^5.
Conclusion
By applying the basic rules of exponents, we were able to simplify a complex expression into a more concise form. Remember to always break down the problem into smaller steps and focus on applying the relevant rules.