%5E5.jpeg "(x^2y)^5")
Understanding (x^2y)^5
In mathematics, expressions involving exponents often require careful simplification. Let's break down the expression (x^2y)^5 and understand its meaning.
The Power of a Product Rule
The core principle at play here is the power of a product rule. This rule states that when raising a product to a power, we raise each factor in the product to that power.
In our case:
(x^2y)^5 = (x^2)^5 * (y)^5
Simplifying the Exponents
Now we have two separate terms with exponents:
- (x^2)^5: When raising a power to another power, we multiply the exponents. So, (x^2)^5 = x^(2*5) = x^10
- (y)^5: This term remains as y^5
The Final Result
Combining the simplified terms, we get the final simplified expression:
(x^2y)^5 = x^10y^5
Key Takeaways
- The power of a product rule is crucial for simplifying expressions with exponents.
- When raising a power to another power, we multiply the exponents.
- Simplifying expressions helps us understand their values and perform further calculations more easily.