How this calculator works
Move the minus sign on the exponent into a reciprocal of the base. It does not move into the sign of the answer. A negative base still changes sign according to the parity of an integer exponent. Reverse modes use the same logarithm and root branches as the math power tool, then require the recovered exponent to be negative. The comparison table shows powers -1 through -5 without computing an oversized positive denominator first.
Formula
b^(-n)=(1/b)^n=1/(b^n), b≠0. For b>0, x=ln(y)/ln(b).
Worked example
2^(-3)=(1/2)^3=1/8. Also (-3)^(-2)=1/9, while (-3)^(-3)=-1/27. A negative exponent alone does not make a result negative.
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Frequently asked questions
Can the base be zero?
No. Its reciprocal would require division by zero.
What if the base is between zero and one?
A negative exponent makes the value greater than one. For example, 0.5^(-3)=8.
Can I recover a negative exponent from any positive value?
No. For base above one the value must be below one; for base between zero and one it must exceed one.