Power of a power, step by step

Raise a power to another power and the exponents multiply: (2³)⁴ is 2¹².

The question

(12⁶)⁵

(12 × 12 × 12 × 12 × 12 × 12) × (12 × 12 × 12 × 12 × 12 × 12) × (12 × 12 × 12 × 12 × 12 × 12) × (12 × 12 × 12 × 12 × 12 × 12) × …

6×5=30

(12⁶)⁵=12³⁰

n=30

(12⁶)⁵ means 5 copies of 12⁶, all multiplied together.
Each copy is 6 12s, and there are 5 copies — so that is 6 × 5 = 30 of them.
30 12s multiplied together is 12³⁰. So n = 30. The shortcut: a power raised to a power MULTIPLIES the exponents.

How it works.

01
(12⁶)⁵ means 5 copies of 12⁶, all multiplied together.
02
Each copy is 6 12s, and there are 5 copies — so that is 6 × 5 = 30 of them.
03
30 12s multiplied together is 12³⁰. So n = 30. The shortcut: a power raised to a power MULTIPLIES the exponents.