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# Exponents and Order of Operations

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

Which part of the expression should be simplified first?
Which of the three boxes should get the largest number?

1 * 4^5

### 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?

Source: Zack Miller (@zmill415)

## Scientific Notation 2

Directions: Using the digits 1 to 9 at most twice each, make the sum of …

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

2. 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.

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

5. 