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(2a^-2b)^-3/5a^2b^4

2 min read Jun 16, 2024
(2a^-2b)^-3/5a^2b^4

Simplifying the Expression: (2a^-2b)^-3/5a^2b^4

This article will guide you through the process of simplifying the given expression: (2a^-2b)^-3/5a^2b^4.

Understanding the Rules

Before diving into the simplification, let's recall some important rules of exponents:

  • Product of powers: x^m * x^n = x^(m+n)
  • Quotient of powers: x^m / x^n = x^(m-n)
  • Power of a power: (x^m)^n = x^(m*n)
  • Negative exponent: x^-n = 1/x^n

Step-by-Step Simplification

  1. Simplify the power of a power: (2a^-2b)^-3 = 2^-3 * a^6 * b^-3

  2. Apply the negative exponent rule: 2^-3 = 1/2^3 = 1/8

  3. Combine terms with the same base: (1/8 * a^6 * b^-3) / (5a^2 * b^4) = (1/40) * (a^(6-2)) * (b^(-3-4))

  4. Simplify the exponents: (1/40) * a^4 * b^-7

  5. Express the negative exponent in the denominator: (a^4)/(40b^7)

Final Result

Therefore, the simplified form of the given expression (2a^-2b)^-3/5a^2b^4 is (a^4)/(40b^7).

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