**Quote:**

If you look at the first problem in the example "Factor: 7² + 7^5", the provided answer of 7²(1 + 7³), this says that (7²)(7³) = 7^5. So why wouldn't (3²)(4²) = 12^4?

Take a look at these examples with factors instead of powers:

7² + 7^5 = 7 × 7 + 7 × 7 × 7 × 7 × 7 = (7 × 7)(1 + 7 × 7 × 7) = 7² (1 + 7³)

3² + 12² = 3 × 3 + (3 × 4)² = 3 × 3 + 3 × 3 × 4 × 4 = (3 × 3)(1 + 4 × 4) = 3² (1 + 4²)

**Quote:**

…, this says that (7²)(7³) = 7^5. So why wouldn't (3²)(4²) = 12^4?

In (7²)(7³) = 7^5 the factors have the same base, so we add the powers.

(7 × 7)(7 × 7 × 7) = 7^5

In (3²)(4²) = 12² the factors have the same powers, so we multiply the bases.

(3 × 3)(4 × 4) = (3 × 4)(3 × 4) = (3 × 4)² = 12²