Calculate x raised to the power n for any base and exponent including integers, fractions, negatives, and zero. View scientific notation, digit count, powers table, and growth visualization.
| n | 2ⁿ | Scientific | Even/Odd n |
|---|---|---|---|
| 1 | 2.00 | 2.000e+0 | Odd |
| 2 | 4.00 | 4.000e+0 | Even |
| 3 | 8.00 | 8.000e+0 | Odd |
| 4 | 16.00 | 1.600e+1 | Even |
| 5 | 32.00 | 3.200e+1 | Odd |
| 6 | 64.00 | 6.400e+1 | Even |
| 7 | 128.00 | 1.280e+2 | Odd |
| 8 | 256.00 | 2.560e+2 | Even |
| 9 | 512.00 | 5.120e+2 | Odd |
| 10 | 1,024.00 | 1.024e+3 | Even |
| Rule | Formula | Example |
|---|---|---|
| Product Rule | aⁿ · aᵐ = aⁿ⁺ᵐ | 2³ · 2⁴ = 2⁷ = 128 |
| Quotient Rule | aⁿ / aᵐ = aⁿ⁻ᵐ | 3⁵ / 3² = 3³ = 27 |
| Power of Power | (aⁿ)ᵐ = aⁿᵐ | (2³)² = 2⁶ = 64 |
| Zero Exponent | a⁰ = 1 | 5⁰ = 1 |
| Negative Exponent | a⁻ⁿ = 1/aⁿ | 2⁻³ = 1/8 |
| Fractional Exponent | a^(1/n) = ⁿ√a | 27^(1/3) = 3 |
The Math Power Calculator lets you compute x raised to the power n (xⁿ) for virtually any combination of base and exponent. Whether you're working with positive integers, negative bases, fractional exponents, or zero, the page returns the result together with its scientific notation, digit count, and a full powers table from x¹ through x¹⁰.
Understanding exponentiation is fundamental to algebra and appears everywhere from compound interest formulas and population growth models to physics equations and computer science algorithms. A positive integer exponent means repeated multiplication — for example 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. Negative exponents flip the base into a reciprocal (2⁻³ = 1/8), and fractional exponents represent roots (8^(1/3) = 2).
This calculator supports decimal exponents, fraction input mode (p/q), and provides eight common presets so you can explore results quickly. The interactive growth bar chart shows how fast powers escalate, giving you visual intuition for exponential growth. A built-in power rules reference table covers the product rule, quotient rule, power-of-a-power, zero exponent, and negative exponent identities — everything you need for homework, test prep, or quick engineering checks.
Exponentiation problems change character fast once you move beyond small positive integers. Fractional exponents, negative powers, and very large outputs raise different interpretation questions. This page is useful because it keeps the main result, scientific notation, and size information together, so you can tell not just what xⁿ equals but how that result behaves numerically.
Result = x^n. For fraction exponents p/q: x^(p/q) = (ⁿ√x)^p. Scientific notation: a × 10^k where 1 ≤ |a| < 10.Result: Result (xⁿ) shown by the calculator
Using the preset "2¹⁰", the calculator evaluates the math power calculator — exponentiation (xⁿ) setup, applies the selected algebra rules, and reports Result (xⁿ) with supporting checks so you can verify each transformation.
This calculator takes Base (x), Exponent (n), Exponent Numerator, Exponent Denominator and applies the relevant math power calculator — exponentiation (xⁿ) relationships from your chosen method. It returns both final and intermediate values so you can audit the process instead of treating it as a black box.
Start with the primary output, then use Result (xⁿ), Scientific Notation, Digit Count, Is Integer? to confirm signs, magnitude, and internal consistency. If anything looks off, change one input and compare the updated outputs to isolate the issue quickly.
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Mathematically 0⁰ is considered indeterminate, but by convention in combinatorics and computing it is defined as 1. This calculator follows that convention.
Yes. Switch to "Fraction" input mode and enter the numerator and denominator separately, or type the decimal equivalent in decimal mode.
If the denominator of the exponent is even (like ½), the result is a complex number and this calculator will show no result. Odd roots of negatives (like (-8)^(1/3)) work fine.
JavaScript uses 64-bit floating-point numbers, so results are accurate up to about 15–17 significant digits. Extremely large results may show as Infinity.
It shows the number of digits before the decimal point in the absolute value of the result. For numbers less than 1 (like 0.001) it shows 0.
A negative exponent flips the base into a fraction: x⁻ⁿ = 1 / xⁿ. For example, 2⁻³ = 1/2³ = 1/8 = 0.125.
Simplify exponent expressions using all five rules: product (aⁿ·aᵐ), power of power ((aⁿ)ᵐ), power of product ((ab)ⁿ), quotient (aⁿ/aᵐ), and power of quotient ((a/b)ⁿ). Step-by-step with verification.
Convert numbers to and from scientific notation, perform arithmetic operations (add, subtract, multiply, divide) on scientific numbers, view engineering notation with SI prefixes, and explore magni...
Calculate x raised to the power n for any base and exponent including integers, fractions, negatives, and zero. View scientific notation, digit count, powers table, and growth visualization.