%5E2.jpeg "(3x^4y^3)^2")
Simplifying (3x^4y^3)^2
In mathematics, simplifying expressions is a fundamental skill. Let's explore how to simplify the expression (3x^4y^3)^2.
Understanding Exponent Properties
To simplify this expression, we need to utilize a key property of exponents: (ab)^n = a^n * b^n. This property states that when raising a product to a power, we raise each factor in the product to that power.
Applying the Property
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Apply the property: We can rewrite (3x^4y^3)^2 as 3^2 * (x^4)^2 * (y^3)^2.
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Simplify the exponents: Remember another key property of exponents: (a^m)^n = a^(m*n). Applying this, we get 9 * x^(42) * y^(32).
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Final simplification: Simplifying further, we arrive at 9x^8y^6.
Conclusion
Therefore, the simplified form of (3x^4y^3)^2 is 9x^8y^6. By understanding and applying exponent properties, we can efficiently simplify complex expressions.