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(x^-3)^4

2 min read Jun 17, 2024
(x^-3)^4

Simplifying (x^-3)^4

In mathematics, simplifying expressions is a fundamental skill. One common type of expression involves exponents raised to other exponents. Let's explore how to simplify the expression (x^-3)^4.

Understanding the Rules of Exponents

To simplify this expression, we need to recall some basic rules of exponents:

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

Applying the Rules

  1. Focus on the Inner Exponent: We have x^-3 inside the parentheses. This represents x raised to the power of -3.

  2. Apply the Power of a Power Rule: We raise this entire term (x^-3) to the power of 4. Applying the rule, we get: (x^-3)^4 = x^(-3 * 4)

  3. Simplify the Exponent: -3 * 4 = -12

  4. Final Result: Therefore, (x^-3)^4 simplifies to x^-12.

Additional Notes

While x^-12 is a simplified form, it is often preferred to express answers with positive exponents. We can use the rule x^-n = 1/x^n to rewrite this as 1/x^12.

Understanding and applying the rules of exponents is crucial for simplifying complex expressions and solving mathematical problems. By breaking down expressions into smaller steps and using these rules, you can confidently navigate these types of problems.

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