%5E2.jpeg "(x^3y^7)^2")
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:
- Apply the power of a power rule: (x^3y^7)^2 = x^(32) * y^(72)
- 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.