(-2x%5E-11y%5E-2).jpeg "(-5x^3y^2)(-2x^-11y^-2)")
Simplifying Algebraic Expressions: (-5x^3y^2)(-2x^-11y^-2)
This article will guide you through the simplification of the algebraic expression (-5x^3y^2)(-2x^-11y^-2). We will use the rules of exponents to achieve a concise and simplified form.
Understanding the Rules of Exponents
To effectively simplify the expression, we need to recall the following fundamental rules of exponents:
- Product of powers: x^m * x^n = x^(m+n)
- Negative exponent: x^-n = 1/x^n
Simplifying the Expression
Let's break down the simplification process step-by-step:
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Multiply the coefficients: (-5) * (-2) = 10
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Apply the product of powers rule for 'x': x^3 * x^-11 = x^(3-11) = x^-8
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Apply the product of powers rule for 'y': y^2 * y^-2 = y^(2-2) = y^0
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Simplify y^0: y^0 = 1 (Any non-zero number raised to the power of 0 equals 1)
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Combine the simplified terms: 10 * x^-8 * 1 = 10x^-8
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Express using a positive exponent (optional): 10x^-8 = 10/x^8
Final Result
The simplified form of the expression (-5x^3y^2)(-2x^-11y^-2) is 10x^-8 or 10/x^8.
Conclusion
By utilizing the rules of exponents, we successfully simplified the given algebraic expression. This method can be applied to similar expressions involving multiplication of terms with exponents. Remember to focus on combining coefficients and applying the relevant exponent rules to arrive at the simplest form.