%5E2-simplified.jpeg "(8x^3)^2 Simplified")
Simplifying (8x^3)^2
In mathematics, simplifying expressions is crucial for understanding and solving problems. Let's break down how to simplify the expression (8x^3)^2.
Understanding the Rules
The key to simplifying this expression lies in applying the power of a product rule and the power of a power rule. These rules are:
- Power of a product rule: (ab)^n = a^n * b^n
- Power of a power rule: (a^m)^n = a^(m*n)
Applying the Rules
Let's apply these rules to our expression:
- Apply the power of a product rule: (8x^3)^2 = 8^2 * (x^3)^2
- Apply the power of a power rule: 8^2 * (x^3)^2 = 64 * x^(3*2)
- Simplify: 64 * x^(3*2) = 64x^6
Conclusion
Therefore, the simplified form of (8x^3)^2 is 64x^6. By understanding and applying the fundamental rules of exponents, we can effectively simplify complex expressions and gain a deeper understanding of their meaning.