(-3a%5E2b%5E5).jpeg "(-2ab^3)(-3a^2b^5)")
Simplifying the Expression (-2ab^3)(-3a^2b^5)
In mathematics, simplifying expressions is an important step in solving problems. This involves combining like terms and applying the rules of exponents. Let's break down the simplification of the expression (-2ab^3)(-3a^2b^5).
Understanding the Rules
- Multiplication of variables with exponents: When multiplying variables with the same base, we add their exponents. For example, a^m * a^n = a^(m+n).
- Multiplication of numbers: We multiply the numerical coefficients as usual.
Simplifying the Expression
- Multiply the numerical coefficients: (-2) * (-3) = 6
- Multiply the 'a' terms: a * a^2 = a^(1+2) = a^3
- Multiply the 'b' terms: b^3 * b^5 = b^(3+5) = b^8
Therefore, the simplified expression is 6a^3b^8.
Conclusion
Simplifying expressions like (-2ab^3)(-3a^2b^5) involves applying the fundamental rules of exponents and multiplication. By combining like terms and following the proper order of operations, we can arrive at a simplified expression, in this case, 6a^3b^8. This simplified form is often more convenient for further calculations and analysis.