%5E2.jpeg "(4a^2b^3)^2")
Simplifying (4a^2b^3)^2
This article will explain how to simplify the expression (4a^2b^3)^2.
Understanding the Basics
- Exponents: An exponent indicates how many times a base number is multiplied by itself. For example, x^2 means x * x.
- Power of a product: When raising a product to a power, we raise each factor to that power. For example, (xy)^2 = x^2 * y^2.
Simplifying the Expression
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Apply the power of a product rule: (4a^2b^3)^2 = 4^2 * (a^2)^2 * (b^3)^2
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Simplify each factor: 4^2 = 16 (a^2)^2 = a^(22) = a^4 (b^3)^2 = b^(32) = b^6
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Combine the simplified factors: 16 * a^4 * b^6 = 16a^4b^6
Conclusion
Therefore, the simplified form of (4a^2b^3)^2 is 16a^4b^6. This process demonstrates how to apply the basic rules of exponents to simplify expressions involving multiple variables.