(2x^2y^3)^4

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions with Exponents: (2x²y³)^4

In mathematics, simplifying expressions involving exponents is a fundamental skill. Let's break down how to simplify the expression (2x²y³)^4.

Understanding the Rules of Exponents

Before we begin, let's review some key exponent rules:

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

Simplifying the Expression

1. Apply the Power of a Product Rule:

   (2x²y³)^4 = 2^4 * (x²)^4 * (y³)^4

2. Apply the Power of a Power Rule:

   2^4 * (x²)^4 * (y³)^4 = 16 * x^(24) * y^(34)

3. Simplify:

   16 * x^(24) * y^(34) = 16x⁸y¹²

Conclusion

Therefore, the simplified form of (2x²y³)^4 is 16x⁸y¹². By applying the rules of exponents, we can efficiently simplify expressions involving powers. Understanding these rules is essential for solving various mathematical problems.