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(2x^-1)^3 Without Negative Exponents

2 min read Jun 16, 2024
(2x^-1)^3 Without Negative Exponents

Simplifying (2x^-1)^3 without Negative Exponents

This expression involves both a negative exponent and a power of a power. Let's break it down step-by-step to get rid of the negative exponent:

Understanding the Properties

  • Negative Exponents: A negative exponent indicates the reciprocal of the base raised to the positive version of the exponent. For example, x^-1 = 1/x.
  • Power of a Power: When raising a power to another power, you multiply the exponents. For example, (x^m)^n = x^(m*n).

Applying the Properties to our Expression

  1. Addressing the Negative Exponent: (2x^-1)^3 = (2 * (1/x))^3

  2. Simplifying Inside the Parentheses: (2 * (1/x))^3 = (2/x)^3

  3. Applying the Power of a Power Rule: (2/x)^3 = 2^3 / x^3

  4. Evaluating the Constant: 2^3 / x^3 = 8/x^3

Final Result

Therefore, (2x^-1)^3 simplified without negative exponents is 8/x^3.

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