How this calculator works
For a positive base, multiply the exponents to simplify a nested power. Each original power must exist. Negative bases can break the identity with non-integer outer exponents, so the tool checks both forms and rejects branch changes. Reverse modes recover the positive base or a unique real exponent; a negative base may have multiple roots.
Formula
(b^m)^n = b^(mn) for b > 0. A missing exponent follows mn = ln(value)/ln(b).
Worked example
(2^3)^2 = 2^6 = 64. Also, (4^(1/2))^(-1) = 4^(-1/2) = 1/2.
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Frequently asked questions
Why multiply rather than add the exponents?
The outer power repeats the entire inner power. Adding exponents applies to multiplication of two powers with a common base.
Why can a negative base be rejected?
For example, ((-2)^2)^(1/2) is 2 but (-2)^(2 times 1/2) is -2. The identity does not preserve that branch.
Can a missing exponent be found when the other is zero?
No. A zero exponent removes the dependence on the missing exponent, so a unique answer is unavailable.