Powers of negative numbers and doubling growth
Follow the order of operations with powers, understand the difference between (−3)² and −3², and see why repeated doubling gets large so fast.
- Germany: grade 5
- Iran: grade 7
- Ukraine: grade 7
Guide
This studio follows the Iranian Grade 7 lesson on calculating expressions with powers. The order: 1) brackets 2) powers 3) multiplication and division 4) addition and subtraction (each left to right).
In (−3)2 the base is −3, multiplied by itself twice: (−3)×(−3) = 9. In −32 the base is only 3 and the minus sign comes after the power: −(3×3) = −9.
(3 + 2)2 is not equal to 32 + 22: the first is 52 = 25 and the second is 9 + 4 = 13. But (4×3)2 = 42×32 is true.
A power is for repeated multiplication. If we fold a sheet in half again and again, the number of layers doubles each time: after n folds there are 2n layers.