%5E2-x-(3a%5E2b).jpeg "(-4a^3b^2)^2 X (3a^2b)")
Simplifying Expressions with Exponents
This article will guide you through simplifying the expression (-4a^3b^2)^2 x (3a^2b).
Understanding the Rules
Before we dive into the problem, let's recall some fundamental rules of exponents:
- (a^m)^n = a^(m*n): When raising a power to another power, multiply the exponents.
- a^m * a^n = a^(m+n): When multiplying powers with the same base, add the exponents.
Solving the Expression
-
Simplify the first term: (-4a^3b^2)^2 = (-4)^2 * (a^3)^2 * (b^2)^2 = 16a^6b^4
-
Combine the simplified terms: 16a^6b^4 * 3a^2b = 48a^(6+2)b^(4+1)
-
Final Result: 48a^8b^5
Conclusion
By applying the rules of exponents, we successfully simplified the expression (-4a^3b^2)^2 x (3a^2b) to 48a^8b^5. Remember to break down complex expressions into smaller steps, and always double-check your exponent calculations.