One power stacked on another
Squaring means multiplying a number by itself. Square a power: (2³)². Two copies of 2³ are multiplied.
Set the copies. They open into one long row. Count the row. Then write one power.
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(2³)² — a bracket squared. Step 1 of 4
(2³)²— a bracket squared.- Two copies:
2³ × 2³. - Open the copies into one row: six 2s.
2⁶= 64.
The rule
A power of a power multiplies the exponents. The outside count says how many copies. Two copies of three 2s make six 2s, and 3 × 2 = 6. So (2³)² is 2⁶: 64.
(3²)³=3⁶= 729. Three copies of two 3s make six 3s.(5⁴)²=5⁸. Two copies of four 5s make eight 5s.6⁶=(6²)³=(6³)². One number, written three ways.
Watch out!
Do not add the counts. (2³)² is 2⁶, which is 64. It is not 2⁵, which is 32.