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
