2 min read Jun 17, 2024

Simplifying Expressions with Exponents: (x^3y^7)^2

In mathematics, understanding how to manipulate exponents is crucial for simplifying complex expressions. One common scenario involves raising an entire expression with exponents to another power. Let's delve into simplifying the expression (x^3y^7)^2.

The Power of a Power Rule

The fundamental rule we need here is the power of a power rule: (a^m)^n = a^(m*n). This rule states that when raising a power to another power, you multiply the exponents.

Applying the Rule to Our Expression

Let's apply this rule to our expression (x^3y^7)^2:

  1. Apply the power of a power rule: (x^3y^7)^2 = x^(32) * y^(72)
  2. Simplify the exponents: x^(32) * y^(72) = x^6 * y^14

Final Result

Therefore, the simplified form of (x^3y^7)^2 is x^6 * y^14.

Key Takeaway

By understanding the power of a power rule and applying it correctly, we can efficiently simplify complex expressions involving exponents. This rule is a valuable tool in algebra and beyond, enabling us to manipulate expressions with ease.