(2x^2y^-3)(3x^-1y^5)

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions with Exponents

This article will walk through the steps of simplifying the expression (2x^2y^-3)(3x^-1y^5). We'll use the rules of exponents to arrive at a simplified form.

Understanding the Rules of Exponents

The key to simplifying this expression lies in understanding the following rules of exponents:

• Product of powers: When multiplying exponents with the same base, add the powers.
  • Example: x^m * x^n = x^(m+n)
• Quotient of powers: When dividing exponents with the same base, subtract the powers.
  • Example: x^m / x^n = x^(m-n)
• Power of a power: When raising a power to another power, multiply the powers.
  • Example: (x^m)^n = x^(m*n)
• Negative exponent: A term with a negative exponent can be written as its reciprocal with a positive exponent.
  • Example: x^-n = 1/x^n

Simplifying the Expression

Now, let's apply these rules to our expression:

1. Separate the numerical coefficients and variables: (2x^2y^-3)(3x^-1y^5) = (2 * 3)(x^2 * x^-1)(y^-3 * y^5)

2. Apply the product of powers rule: (2 * 3)(x^2 * x^-1)(y^-3 * y^5) = 6x^(2+(-1))y^(-3+5)

3. Simplify: 6x^(2+(-1))y^(-3+5) = 6x^1y^2

4. Write the final simplified expression: 6x^1y^2 = 6xy^2

Conclusion

Therefore, the simplified form of the expression (2x^2y^-3)(3x^-1y^5) is 6xy^2. By applying the rules of exponents, we can effectively simplify complex expressions and express them in a more concise form.