(-4a%5E2b%5E4).jpeg "(2a^3b^-2)(-4a^2b^4)")
Simplifying Expressions with Exponents
This article will guide you through the process of simplifying the expression (2a^3b^-2)(-4a^2b^4).
Understanding the Basics
Before diving into the simplification, let's review some key concepts about exponents:
- Product of Powers: When multiplying powers with the same base, you add the exponents. For example, x^m * x^n = x^(m+n).
- Negative Exponent: A negative exponent indicates the reciprocal of the base raised to the positive version of the exponent. For example, x^-n = 1/x^n.
Simplifying the Expression
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Distribute: Begin by distributing the multiplication across the parentheses:
(2a^3b^-2)(-4a^2b^4) = 2 * -4 * a^3 * a^2 * b^-2 * b^4
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Combine Coefficients: Multiply the numerical coefficients:
2 * -4 = -8
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Apply Product of Powers: Combine the terms with the same base by adding the exponents:
a^3 * a^2 = a^(3+2) = a^5 b^-2 * b^4 = b^(-2+4) = b^2
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Final Expression: Put it all together:
-8 * a^5 * b^2 = -8a^5b^2
Conclusion
The simplified form of (2a^3b^-2)(-4a^2b^4) is -8a^5b^2. Remember the key rules of exponents to simplify these types of expressions efficiently.