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(a^-5)^2 Simplified

2 min read Jun 16, 2024
(a^-5)^2 Simplified

Simplifying (a^-5)^2

In mathematics, simplifying expressions is a crucial skill. This involves using the rules of exponents to express the expression in its simplest form. Today, we'll tackle the simplification of (a^-5)^2.

Understanding the Rules

Before we dive into the simplification, let's review the essential rules of exponents we'll use:

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

Simplifying (a^-5)^2

Now, let's apply these rules to our expression:

  1. Apply the Power of a Power rule: (a^-5)^2 = a^(-5*2)

  2. Simplify the exponent: a^(-5*2) = a^-10

  3. Apply the Negative Exponent rule: a^-10 = 1/a^10

Therefore, the simplified form of (a^-5)^2 is 1/a^10.

Conclusion

Simplifying expressions like (a^-5)^2 involves understanding and applying the fundamental rules of exponents. By systematically applying these rules, we can arrive at a concise and easy-to-understand expression.

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