## Simplifying (7y^4)^2

In mathematics, simplifying expressions is a crucial skill. One common type of simplification involves exponents. Let's break down how to simplify the expression (7y^4)^2.

### Understanding Exponents

An exponent indicates how many times a base number is multiplied by itself. In this case, we have:

**Base:**7y^4**Exponent:**2

This means we are multiplying the entire base (7y^4) by itself twice.

### Applying the Power of a Product Rule

To simplify the expression, we can use the **Power of a Product Rule**. This rule states that when raising a product to a power, we raise each factor to that power. Mathematically, this is represented as:

**(ab)^n = a^n * b^n**

Applying this rule to our expression:

(7y^4)^2 = 7^2 * (y^4)^2

### Applying the Power of a Power Rule

We now have another exponent within our expression: (y^4)^2. To simplify this, we use the **Power of a Power Rule**. This rule states that when raising a power to another power, we multiply the exponents. Mathematically:

**(a^m)^n = a^(m*n)**

Applying this rule to our expression:

7^2 * (y^4)^2 = 7^2 * y^(4*2)

### Final Simplification

Now, we can simply calculate the remaining exponents:

7^2 * y^(4*2) = 49y^8

Therefore, the simplified form of (7y^4)^2 is **49y^8**.