(2/5ab)5 (1/3ab)3

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions with Exponents

This article will guide you through simplifying the expression (2/5ab)^5 (1/3ab)^3. We'll use the rules of exponents to break down the problem step by step.

Understanding the Rules of Exponents

Before we dive into the simplification, let's refresh our memory on the key exponent rules we'll be using:

• Product of powers: (a^m) * (a^n) = a^(m+n)
• Power of a product: (ab)^n = a^n * b^n
• Power of a quotient: (a/b)^n = a^n / b^n

Simplifying the Expression

1. Apply the power of a quotient rule:

   (2/5ab)^5 = 2^5 / (5ab)^5 (1/3ab)^3 = 1^3 / (3ab)^3

2. Apply the power of a product rule:

   (5ab)^5 = 5^5 * a^5 * b^5 (3ab)^3 = 3^3 * a^3 * b^3

3. Substitute the simplified terms back into the original expression:

   (2^5 / (5^5 * a^5 * b^5)) * (1^3 / (3^3 * a^3 * b^3))

4. Simplify the numerical values:

   (32 / (3125 * a^5 * b^5)) * (1 / (27 * a^3 * b^3))

5. Apply the product of powers rule:

   (32 * 1) / (3125 * 27 * a^(5+3) * b^(5+3))

6. Final simplification:

   32 / (84375 * a^8 * b^8)

Conclusion

By applying the rules of exponents, we successfully simplified the expression (2/5ab)^5 (1/3ab)^3 to 32 / (84375 * a^8 * b^8). Remember to always break down complex expressions into smaller, manageable steps. This approach helps ensure accuracy and a clear understanding of the simplification process.