%5E2.jpeg "(x^4y^3)^2")
Simplifying (x^4y^3)^2
In mathematics, simplifying expressions is a fundamental skill. This article will guide you through the process of simplifying the expression (x^4y^3)^2.
Understanding the Laws of Exponents
To tackle this expression, we need to understand the following laws of exponents:
- Product of powers: x^m * x^n = x^(m+n)
- Power of a product: (x * y)^n = x^n * y^n
- Power of a power: (x^m)^n = x^(m*n)
Simplifying the Expression
Let's break down the simplification step-by-step:
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Apply the power of a product rule: (x^4y^3)^2 = (x^4)^2 * (y^3)^2
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Apply the power of a power rule: (x^4)^2 * (y^3)^2 = x^(42) * y^(32)
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Simplify: x^(42) * y^(32) = x^8y^6
Conclusion
Therefore, the simplified form of (x^4y^3)^2 is x^8y^6. This process demonstrates how to use the laws of exponents to simplify expressions involving powers of variables.