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.
- إيران: الصف ٧
- أوكرانيا: الصف ٧
- ألمانيا: الصف ٥
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
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 (−٣)٢ the base is −٣, multiplied by itself twice: (−٣)×(−٣) = ٩. In −٣٢ the base is only 3 and the minus sign comes after the power: −(٣×٣) = −٩.
(٣ + ٢)٢ is not equal to ٣٢ + ٢٢: the first is ٥٢ = ٢٥ and the second is ٩ + ٤ = ١٣. But (٤×٣)٢ = ٤٢×٣٢ is true.
A قوة 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 ٢n layers.