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

Applying the power of a product rule:
 (u^4v^3)^2 = (u^4)^2 * (v^3)^2

Applying the power of a power rule:
 (u^4)^2 * (v^3)^2 = u^(42) * v^(32)

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.