(2x^4)^-3

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

Simplifying (2x^4)^-3

This expression involves both exponents and parentheses, so we need to apply the rules of exponents in the correct order. Here's how we simplify it:

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

Step-by-Step Simplification

  1. Apply the Power of a Product rule: (2x^4)^-3 = 2^-3 * (x^4)^-3

  2. Apply the Power of a Power rule: 2^-3 * (x^4)^-3 = 2^-3 * x^(4*-3) = 2^-3 * x^-12

  3. Apply the Negative Exponent rule: 2^-3 * x^-12 = 1/2^3 * 1/x^12

  4. Simplify: 1/2^3 * 1/x^12 = 1/8 * 1/x^12 = 1/(8x^12)

Conclusion

Therefore, the simplified form of (2x^4)^-3 is 1/(8x^12).

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