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Power to a power to a power

What is raising a power to a power to a power?

Raising a power to a power to a power:

((ak)m)n =
ak * m * n

See Power to a power definition.

Power to a power to a power examples

Example 1.

Power to a power to a power

((ab)c)d = ab * c * d

Example 2.

Power to a power to a power

((22)3)2 =
22 * 3 * 2 =
212 = 4096

See Powers of 2.

Example 3.

Power of a power of a power of a sum

((1 + 2)3)2)2 =
(1 + 2)3 * 2 * 2 =
312 = 531441

See Powers of 3.

Example 4.

Power of a power of a power of a product

((22 * 32)3)2 =
((2 * 3)2)3)2 =
62 * 3 * 2 =
612

See Powers of 6.