## Simplifying the Expression (7a^2)(5a^6b)^2

In mathematics, simplifying expressions involves rewriting them in their most basic and compact form. Let's explore how to simplify the expression **(7a^2)(5a^6b)^2**.

### Understanding the Properties

To simplify this expression, we need to understand the following properties:

**Power of a product:**(ab)^n = a^n * b^n**Power of a power:**(a^m)^n = a^(m*n)

### Step-by-Step Simplification

**Simplify the inner power:**(5a^6b)^2 = 5^2 * (a^6)^2 * b^2 = 25a^12b^2**Multiply the simplified inner power by the term outside:**(7a^2)(25a^12b^2) = 7 * 25 * a^2 * a^12 * b^2**Combine like terms:**175a^(2+12)b^2**Simplify the exponents:**175a^14b^2

### The Final Simplified Expression

Therefore, the simplified form of (7a^2)(5a^6b)^2 is **175a^14b^2**.