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(x^4)^-3 * 2x^4

less than a minute read Jun 17, 2024
(x^4)^-3 * 2x^4

Simplifying the Expression: (x^4)^-3 * 2x^4

This expression involves the concepts of exponents and their properties. Let's break it down step-by-step to simplify it:

Understanding the Properties

  • Power of a power: (x^m)^n = x^(m*n)
  • Product of powers: x^m * x^n = x^(m+n)

Simplifying the Expression

  1. Apply the power of a power rule to the first term: (x^4)^-3 = x^(4*-3) = x^-12

  2. Now we have: x^-12 * 2x^4

  3. Apply the product of powers rule: x^-12 * 2x^4 = 2 * x^(-12+4) = 2x^-8

  4. Express the negative exponent as a positive one: 2x^-8 = 2 / x^8

Final Answer: The simplified form of the expression (x^4)^-3 * 2x^4 is 2/x^8.

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