Calculate powers or solve for a real base or exponent, with exact integer and rational results, perfect-root checks and transparent approximate forms.
01 / REAL POWERS & INVERSES
Use integers, signed decimals, p/q fractions, scientific notation such as 1e3, or the constant e. Calculations run when you choose Calculate.
02 / MATHEMATICAL WORKING
(2)10
= 1024
Integer power: repeated multiplication; a^0 = 1 for nonzero a.
1024
Real-number mode only. 0⁰ is treated as undefined/indeterminate. Decimal exponents are exact finite decimals; enter 1/3 to mean one third, not a rounded decimal approximation.
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Review the explanation, copy supported outputs or reset the workspace.
Choose result, base or exponent; enter the known values and select Calculate. Use p/q for an exact rational exponent, then inspect the worked expression and exact-versus-approximate labels.
Preserve exact integer and fraction results, check real-root domains, and distinguish unevaluated radicals from decimal approximations. Formatted powers and worked root substitutions explain signs, reciprocals and multiple inverse solutions.
Mathematical expressions and exact-number calculations are processed locally in browser memory. No expression is submitted to a remote solver or stored in an account. Copy a result only when you want it on your clipboard.
Yes, within documented bounds. BigInt rational arithmetic preserves exact digits, including negative integer powers as simplified reciprocals. Exact storage is conservatively bounded to roughly 12,000 digits; oversized or nonfinite approximate calculations are not silently labeled exact.
A fraction p/q is reduced before checking roots. Perfect integer roots of numerator and denominator are detected for root degree up to 100, then raised exactly. Non-perfect roots use labeled real-number approximations.
A reduced rational exponent with an odd denominator can have a real result, such as (-8)^(1/3) = -2 and (-8)^(2/3) = 4. Even-denominator roots of negative values are rejected in real mode. A finite decimal approximation to one third is not treated as exact one third.
Even powers can lose the sign of the base. For a² = 16, both +4 and -4 solve the equation. The calculator checks the rational exponent domain and explicitly reports both real branches when applicable.
For nonzero a, a^0 = 1. This calculator treats 0^0 as undefined/indeterminate, and zero raised to a negative exponent is undefined because it would divide by zero. Inverse problems that lack a unique answer are explained instead of guessed.
For a positive base other than one and a positive result, b = ln(x)/ln(a). Integer candidates are verified by exact rational powers when possible. 1^b = 1 is non-unique, and negative-base exponent inversion is withheld because its rational domain is not a continuous real logarithm.