(-a^2b^3)^2*(4a^3b^2)+9a^7b^8

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions: (-a^2b^3)^2*(4a^3b^2)+9a^7b^8

This article will guide you through simplifying the algebraic expression (-a^2b^3)^2(4a^3b^2)+9a^7b^8*.

Understanding the Rules

Before we begin, let's recall some fundamental rules of exponents:

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

Step-by-Step Simplification

1. Simplify the first term:

   • Apply the Power of a Product rule: (-a^2b^3)^2 = (-1)^2 * (a^2)^2 * (b^3)^2
   • Apply the Power of a Power rule: (-1)^2 * (a^2)^2 * (b^3)^2 = 1 * a^4 * b^6
   • Multiply by the remaining factors: 1 * a^4 * b^6 * (4a^3b^2) = 4a^7b^8

2. Combine the simplified terms:

   • 4a^7b^8 + 9a^7b^8

3. Apply the Product of Powers rule:

   • 4a^7b^8 + 9a^7b^8 = (4+9)a^7b^8

4. Final simplification:

   • (4+9)a^7b^8 = 13a^7b^8

Conclusion

Therefore, the simplified form of the expression (-a^2b^3)^2*(4a^3b^2)+9a^7b^8 is 13a^7b^8. By applying the fundamental rules of exponents, we successfully simplified the expression.