(2x^3y^2/3xy)^-3

Jasonbradley

3 min read

·

Jun 16, 2024

16

Share

Simplifying Expressions with Negative Exponents: A Step-by-Step Guide

This article will guide you through the process of simplifying the expression (2x^3y^2/3xy)^-3.

Understanding Negative Exponents

Before we dive into the simplification, let's quickly recap the concept of negative exponents.

A negative exponent signifies the reciprocal of the base raised to the positive value of the exponent. In other words, x^-n = 1/x^n.

Simplifying the Expression

1. Apply the Power of a Quotient Rule:

   • This rule states that (a/b)^n = a^n/b^n.
   • Applying this rule, we get: (2x^3y^2/3xy)^-3 = (2x^3y^2)^-3 / (3xy)^-3

2. Apply the Power of a Product Rule:

   • This rule states that (ab)^n = a^n * b^n.
   • Applying this rule to both numerator and denominator, we get: (2^-3 * x^(3-3) * y^(2-3)) / (3^-3 * x^-3 * y^-3)**

3. Simplify the Exponents:

   • We now have: (1/2^3 * x^-9 * y^-6) / (1/3^3 * x^-3 * y^-3)

4. Rearrange and Simplify Using the Negative Exponent Rule:

   • We can rewrite this as: (3^3 * x^3 * y^3) / (2^3 * x^9 * y^6)
   • Simplifying further: (27x^3y^3) / (8x^9y^6)

5. Simplify by Subtracting Exponents:

   • Using the rule a^m/a^n = a^(m-n), we get: (27/8) * x^(3-9) * y^(3-6)

6. Final Simplified Expression:

   • The final simplified expression is: (27/8)x^-6y^-3

Conclusion

By following these steps, we have successfully simplified the expression (2x^3y^2/3xy)^-3 to (27/8)x^-6y^-3. Remember, understanding the rules of exponents is crucial for manipulating and simplifying complex expressions.