%5E2.jpeg "(7y^3)^2")
Simplifying (7y^3)^2
In mathematics, simplifying expressions is a key skill. One common type of simplification involves exponents. Let's explore how to simplify the expression (7y^3)^2.
Understanding the Rules
The core principle here is the power of a product rule: (ab)^n = a^n * b^n. This rule tells us that when we raise a product to a power, we raise each factor in the product to that power.
Applying the Rule
- Identify the factors: In our expression (7y^3)^2, we have two factors: 7 and y^3.
- Apply the power to each factor: (7y^3)^2 = 7^2 * (y^3)^2
- Simplify further: 7^2 = 49 and (y^3)^2 = y^(3*2) = y^6
The Final Result
Therefore, the simplified expression is 49y^6.
Key Takeaway: Remember to apply the power of a product rule carefully when simplifying expressions involving exponents and products.