%5E2%2F24x%5E3y%5E2.jpeg "(4x^4y)^2/24x^3y^2")
Simplifying Algebraic Expressions: (4x^4y)^2 / 24x^3y^2
This article will guide you through the steps of simplifying the algebraic expression (4x^4y)^2 / 24x^3y^2. We will utilize the rules of exponents to break down the expression and arrive at a simplified form.
Understanding the Rules of Exponents
Before we dive into the simplification, let's review the key exponent rules we'll be using:
- Power of a product: (ab)^n = a^n * b^n
- Power of a power: (a^m)^n = a^(m*n)
- Division of exponents with the same base: a^m / a^n = a^(m-n)
Simplifying the Expression
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Apply the power of a product rule to the numerator: (4x^4y)^2 = 4^2 * (x^4)^2 * y^2 = 16x^8y^2
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Apply the power of a power rule to the numerator: 16x^8y^2 = 16x^(4*2)y^2 = 16x^8y^2
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Combine the simplified numerator with the denominator: (16x^8y^2) / (24x^3y^2)
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Apply the division of exponents rule to the variables: 16x^(8-3)y^(2-2) / 24 = 16x^5y^0 / 24
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Simplify the exponents and coefficients: 16x^5 / 24 = (2/3)x^5
Conclusion
Therefore, the simplified form of the expression (4x^4y)^2 / 24x^3y^2 is (2/3)x^5. By applying the rules of exponents, we were able to break down the expression and arrive at a concise and simplified result. Remember that understanding and utilizing these rules is essential for efficiently simplifying algebraic expressions.