(-3x^4y^3)^4

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions with Exponents: (-3x^4y^3)^4

This article will guide you through simplifying the expression (-3x^4y^3)^4. Understanding how to deal with exponents and their properties is crucial in algebra and beyond.

Key Properties of Exponents

Before we dive into the simplification, let's recall some essential exponent rules:

• 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 (-3x^4y^3)^4

1. Apply the Power of a Product rule:

   We have a product inside the parentheses, so we apply the rule:

   (-3x^4y^3)^4 = (-3)^4 * (x^4)^4 * (y^3)^4

2. Simplify each term:

   • (-3)^4 = 81
   • (x^4)^4 = x^(4*4) = x^16
   • (y^3)^4 = y^(3*4) = y^12

3. Combine the results:

   81 * x^16 * y^12 = 81x^16y^12

Conclusion

Therefore, the simplified form of (-3x^4y^3)^4 is 81x^16y^12. By applying the appropriate exponent rules, we can efficiently simplify complex expressions like this one.