(-a^2)^4 X (3ab^5)^3

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions with Exponents

This article will guide you through simplifying the expression (-a^2)^4 x (3ab^5)^3. We'll use the rules of exponents to break down the problem step by step.

Understanding the Rules

Before we dive into the problem, let's refresh our memory on the key rules 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 the Expression

Now, let's apply these rules to our expression:

1. Simplify (-a^2)^4:

   • Using the power of a power rule: (-a^2)^4 = (-1)^4 * (a^2)^4 = 1 * a^(2*4) = a^8

2. Simplify (3ab^5)^3:

   • Using the power of a product rule: (3ab^5)^3 = 3^3 * a^3 * (b^5)^3
   • Using the power of a power rule: 3^3 * a^3 * (b^5)^3 = 27 * a^3 * b^(5*3) = 27a^3b^15

3. Multiply the simplified terms:

   • a^8 * 27a^3b^15 = 27a^(8+3)b^15 = 27a^11b^15

Conclusion

Therefore, the simplified form of (-a^2)^4 x (3ab^5)^3 is 27a^11b^15. Remember to apply the rules of exponents carefully, paying close attention to the signs and powers.