(2ab)^5

Jasonbradley

2 min read

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Jun 16, 2024

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Simplifying (2ab)^5

In mathematics, simplifying expressions is crucial for understanding and working with them. One common type of simplification involves dealing with exponents, especially when they involve multiple variables. Today, we will explore how to simplify the expression (2ab)^5.

Understanding the Properties of Exponents

Before we dive into the simplification process, let's recall the key properties of exponents:

• Product of Powers: x^m * x^n = x^(m+n)
• Power of a Product: (xy)^n = x^n * y^n
• Power of a Power: (x^m)^n = x^(m*n)

Simplifying (2ab)^5

1. Apply the Power of a Product Property:

   We can apply the Power of a Product Property to expand the expression:

   (2ab)^5 = 2^5 * a^5 * b^5

2. Calculate the Exponent of the Constant:

   Calculate 2^5, which is 2 * 2 * 2 * 2 * 2 = 32.

3. Final Simplified Expression:

   The simplified expression becomes: 32a^5b^5

Conclusion

By applying the properties of exponents, we were able to effectively simplify the expression (2ab)^5 into 32a^5b^5. This simplification makes it easier to understand and work with the expression in further calculations. Remember to always apply the properties of exponents carefully and systematically for accurate results.