(10^2)^-3 As A Single Exponent

2 min read Jun 16, 2024
(10^2)^-3 As A Single Exponent

Simplifying (10^2)^-3 as a Single Exponent

In mathematics, simplifying expressions is often crucial for understanding and manipulating them effectively. One common type of simplification involves combining exponents. Let's explore how to express (10^2)^-3 as a single exponent.

Understanding the Rules of Exponents

To simplify this expression, we'll utilize two key rules of exponents:

  • Power of a Power: (a^m)^n = a^(m*n)
  • Negative Exponent: a^-n = 1/a^n

Applying the Rules

  1. Applying the Power of a Power Rule: (10^2)^-3 = 10^(2*-3)

  2. Simplifying the Exponent: 10^(2*-3) = 10^-6

  3. Applying the Negative Exponent Rule: 10^-6 = 1/10^6

Therefore, (10^2)^-3 can be simplified as a single exponent 1/10^6.

Key Takeaways

  • By applying the appropriate exponent rules, we can effectively combine exponents and simplify complex expressions.
  • Understanding the relationship between exponents and their reciprocals is essential for working with negative exponents.

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