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Power Equation Solver & Exponent Calculator (Steps + Graph)

Solve x^n = a and calculate powers with step-by-step algebra. Supports BigInt for large numbers, fractional exponents, and visual curve plotting.

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Category Academic Calculators
Base (a)^Exponent (n)=?
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About

Algebraic power equations form the backbone of exponential growth modeling, physics, and compound interest calculations. This tool is engineered to solve two distinct classes of problems: evaluating exponentials (an) and solving for roots in power equations (xn = a). Unlike standard calculators that round immediately to scientific notation, this engine employs BigInt logic to preserve precision for astronomically large integers where possible. It generates a dynamic curve graph to visually demonstrate the geometry of the solution-critical for understanding why even roots have two solutions (±) while odd roots have one.

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Formulas

To solve for the base x in the equation xn = a, we apply the inverse exponent 1n to both sides:

x = a1n

If n is an even integer, the solution branches:

{
x = √ax = −√a

Reference Data

OperationEquation TypeInverse OperationDomain Restrictions
Squarey = x2x = ±√yy ≥ 0 for real roots
Cubey = x3x = ∛yAll Real Numbers (R)
n-th Powery = xnx = y1/nDepends on parity of n
Exponentialy = bxx = logb(y)b > 0

Frequently Asked Questions

Because a negative number multiplied by itself an even number of times results in a positive number (e.g., (-2)^2 = 4). Therefore, when solving x^2 = 4, both 2 and -2 are valid solutions.
In the set of Real Numbers (R), this is impossible, and the result is "undefined" or NaN. In the set of Complex Numbers (C), the result involves "i" (imaginary unit), but this tool focuses on Real number solutions.
Yes. You can calculate values like 25^0.5, which is equivalent to the square root of 25 (Result: 5). The solver handles decimal inputs for both base and exponent.