Power calculator
Base can be a decimal, fraction, e or pi. Exponent can also be a fraction like 1/3.
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Real-domain rule: a negative base with a reduced rational exponent p/q has a real value when q is odd. Otherwise this tool shows the principal complex value instead of pretending the real result exists.
Result
Ready to calculate.
power
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Scientific
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log₁₀ |result|
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Reciprocal
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Type
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Calculation steps appear here.
Product of powers
Quotient of powers
Power of a power
Inverse power solver: fill any two values in aⁿ = y and leave exactly one blank. Solving for n uses the real logarithmic branch and therefore requires a positive base a ≠ 1 and y > 0.
Solved relationship
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Fast modular exponentiation: computes base^exponent mod modulus with BigInt repeated squaring, so very large integer exponents do not require constructing the enormous full power.
Result
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For a positive base, the table shows a^x across the selected integer range.
Core exponent laws:
aᵐ·aⁿ = aᵐ⁺ⁿ
aᵐ/aⁿ = aᵐ⁻ⁿ (a≠0)
(aᵐ)ⁿ = aᵐⁿ
a⁻ⁿ = 1/aⁿ
a^(p/q) = qth-root(aᵖ), with real-domain restrictions for negative a.
aᵐ·aⁿ = aᵐ⁺ⁿ
aᵐ/aⁿ = aᵐ⁻ⁿ (a≠0)
(aᵐ)ⁿ = aᵐⁿ
a⁻ⁿ = 1/aⁿ
a^(p/q) = qth-root(aᵖ), with real-domain restrictions for negative a.