(u^4v^3)^2

Jasonbradley

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Jun 16, 2024

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Simplifying (u^4v^3)^2

In mathematics, simplifying expressions is a crucial skill. Today, we'll explore how to simplify the expression (u^4v^3)^2.

Understanding the Rules of Exponents

To simplify this expression, we need to understand a couple of key exponent rules:

• Power of a product: (ab)^n = a^n * b^n
• Power of a power: (a^m)^n = a^(m*n)

Applying the Rules to Simplify

1. Applying the power of a product rule:

   • (u^4v^3)^2 = (u^4)^2 * (v^3)^2

2. Applying the power of a power rule:

   • (u^4)^2 * (v^3)^2 = u^(42) * v^(32)

3. Simplifying:

   • u^(42) * v^(32) = u^8v^6

Conclusion

Therefore, the simplified form of (u^4v^3)^2 is u^8v^6. Remember, understanding the rules of exponents is essential for simplifying complex expressions in algebra and beyond.