Power Symmetry 2

Transitive Property of Equality Variation 1

Propagated Transitive Property 3

Logofpower

Transitive Property of Equality Variation 2

Transitive Property Application 2

Converseofpowersubstitution

Move Terms Around

Logofpowerdifferentbase

Proof: Power Symmetry 2

Let's prove the following theorem:

x^{(m ⋅ n)} = (x^m)ⁿ

Proof:

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Proof Table

#	Claim	Reason
1	(x^m)ⁿ = x^{(m ⋅ n)}	(x^m)ⁿ = x^{(m ⋅ n)} (Power of a Power)
2	x^{(m ⋅ n)} = (x^m)ⁿ	if (x^m)ⁿ = x^{(m ⋅ n)}, then x^{(m ⋅ n)} = (x^m)ⁿ (Symmetric Property of Equality)

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