**Evaluating the Expression: 7² × 2⁸ + 7³ × 7²**

To evaluate this expression, we need to follow the order of operations (PEMDAS):

**Exponents****Multiplication and Division**(from left to right)**Addition and Subtraction**(from left to right)

Let's break down the expression:

### Evaluating the Exponents

First, we need to evaluate the exponents:

- 7² = 7 × 7 =
**49** - 2⁸ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 =
**256** - 7³ = 7 × 7 × 7 =
**343** - 7² = 7 × 7 =
**49**(same as the first one)

### Evaluating the Multiplication

Next, we need to multiply the numbers:

- 49 × 256 =
**12,544** - 343 × 49 =
**16,807**

### Evaluating the Addition

Finally, we add the two results:

- 12,544 + 16,807 =
**29,351**

Therefore, the final answer is:

**7² × 2⁸ + 7³ × 7² = 29,351**