Directions: Find 3 positive integers that add up to 10. Place each number into one of the blanks to find the largest possible result.

### Hint

### Hint

Which part of the expression should be simplified first?

Which of the three boxes should get the largest number?

Which of the three boxes should get the largest number?

### Answer

### Answer

1 * 4^5

### Extensions

### Extensions

There are many extensions with the exact same prompt:

1. What’s the smallest possible result?

2. What if you’re working with all integers greater than (-5)?

3. How close can you get to 0 without hitting it exactly?

1. What’s the smallest possible result?

2. What if you’re working with all integers greater than (-5)?

3. How close can you get to 0 without hitting it exactly?

Source: Zack Miller (@zmill415)

(2×3)^5 results in a larger number than (1×4)^5

Oops, didn’t see the comment thread above. The order of operations says we do the exponents first, so:

2 x 3^5 < 1 * 4^5

I’m not sure if you noticed, Zack and Julie: Julie changed the position of the brackets. With that change, her answer is correct. However, with the original brackets, Zack is correct.

1 * 4^5

(2×3)^5 results in a larger number than (1×4)^5

1*4^5