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(5s^-2t^4)^-3

less than a minute read Jun 16, 2024
(5s^-2t^4)^-3

Simplifying (5s^-2t^4)^-3

This expression involves several rules of exponents. Let's break it down step by step.

Understanding the Rules

  • Power of a Product: (ab)^n = a^n * b^n
  • Power of a Power: (a^m)^n = a^(m*n)
  • Negative Exponent: a^-n = 1/a^n

Applying the Rules

  1. Distribute the outer exponent: (5s^-2t^4)^-3 = 5^-3 * (s^-2)^-3 * (t^4)^-3

  2. Simplify each term:

    • 5^-3 = 1/5^3 = 1/125
    • (s^-2)^-3 = s^(-2*-3) = s^6
    • (t^4)^-3 = t^(4*-3) = t^-12

  3. Combine the terms: 1/125 * s^6 * t^-12

  4. Rewrite the term with a negative exponent: 1/125 * s^6 * (1/t^12)

  5. Simplify further: s^6 / (125t^12)

Final Answer

Therefore, the simplified expression of (5s^-2t^4)^-3 is s^6 / (125t^12).

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