(2x^-1)^3

Jasonbradley

2 min read

·

Jun 16, 2024

9

Share

Simplifying (2x^-1)^3

This expression involves several concepts in algebra, including exponents, negative exponents, and the power of a product rule. Let's break it down step by step.

Understanding the Components

• (2x^-1): This is a product of two terms: 2 and x^-1.
• ^3: This indicates that the entire expression (2x^-1) is raised to the power of 3.

Applying the Rules

1. Power of a Product Rule: When raising a product to a power, we raise each factor to that power. So, (2x^-1)^3 = 2^3 * (x^-1)^3

2. Power of a Power Rule: When raising a power to another power, we multiply the exponents. Therefore, (x^-1)^3 = x^(-1*3) = x^-3

Simplifying the Expression

Putting it all together, we get:

(2x^-1)^3 = 2^3 * x^-3 = 8 * x^-3

Negative Exponent

Remember that a negative exponent indicates the reciprocal of the base raised to the positive version of that exponent. Therefore:

x^-3 = 1/x^3

Final Result

Therefore, the simplified form of (2x^-1)^3 is:

(2x^-1)^3 = 8/x^3