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(3a^-2b)^3

2 min read Jun 16, 2024
(3a^-2b)^3

Simplifying the Expression (3a^-2b)^3

This article will guide you through simplifying the expression (3a^-2b)^3.

Understanding the Rules

To simplify this expression, we need to apply a few key exponent rules:

  • Power of a Product: (ab)^n = a^n * b^n
  • Power of a Quotient: (a/b)^n = a^n / b^n
  • Power of a Power: (a^m)^n = a^(m*n)

Applying the Rules

Let's break down the simplification step-by-step:

  1. Apply the Power of a Product Rule: (3a^-2b)^3 = 3^3 * (a^-2)^3 * b^3

  2. Apply the Power of a Power Rule: 3^3 * (a^-2)^3 * b^3 = 27 * a^(-2*3) * b^3

  3. Simplify the exponents: 27 * a^(-2*3) * b^3 = 27 * a^-6 * b^3

  4. Rewrite with positive exponents: 27 * a^-6 * b^3 = 27b^3 / a^6

Conclusion

Therefore, the simplified form of the expression (3a^-2b)^3 is 27b^3 / a^6.

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