(2^3x^2)^5

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (2^3x^2)^5

This article will guide you through simplifying the expression (2^3x^2)^5. We'll break down the process step by step, explaining the rules of exponents used.

Understanding the Rules of Exponents

Before we dive into simplification, let's review the relevant rules of exponents:

• Product of Powers: (a^m) * (a^n) = a^(m+n)
• Power of a Power: (a^m)^n = a^(m*n)
• Power of a Product: (ab)^n = a^n * b^n

Simplifying the Expression

1. Apply the Power of a Power Rule:
   We begin by applying the Power of a Power rule to the entire expression:

   (2^3x^2)^5 = 2^(35) * x^(25)

2. Simplify the Exponents: Next, we multiply the exponents:

   2^(35) * x^(25) = 2^15 * x^10

3. Final Result: The simplified expression is 2^15 * x^10.

Conclusion

By applying the rules of exponents, we have successfully simplified the expression (2^3x^2)^5 to 2^15 * x^10. Remember, understanding these rules is crucial for manipulating and simplifying exponential expressions in various mathematical contexts.