{
    "name": "Exponent Calculator",
    "url": "https://calculators.geekmidst.com/calculators/exponent-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/exponent-calculator.md",
    "category": "Mathematics",
    "description": "Calculate bⁿ for any base and exponent, including negative and fractional powers. Whole-number powers are exact to hundreds of digits.",
    "summary": "Raise a number to any power. Whole-number answers are calculated exactly, digit for digit, and very large or small results are also shown in scientific notation.",
    "also_called": [
        "Power calculator",
        "Indices calculator"
    ],
    "applies_to": "Worldwide",
    "last_updated": "2026-10-29",
    "computation": "Results are computed in the visitor’s browser on the HTML page. This API describes the calculator; it does not compute results.",
    "inputs": [
        {
            "name": "base",
            "label": "Base (b)",
            "type": "number",
            "default": "2"
        },
        {
            "name": "exponent",
            "label": "Exponent (n)",
            "type": "number",
            "default": "10"
        }
    ],
    "outputs": [
        {
            "key": "result",
            "label": "bⁿ",
            "format": "text"
        },
        {
            "key": "scientific",
            "label": "Scientific notation",
            "format": "text"
        }
    ],
    "formula": {
        "text": "bⁿ = b × b × … × b (n times);  b⁻ⁿ = 1 ÷ bⁿ;  b^(1/k) = the kth root of b;  b⁰ = 1",
        "variables": {
            "b": "the base",
            "n": "the exponent (power or index)"
        }
    },
    "worked_example": {
        "inputs": {
            "base": "2",
            "exponent": "10"
        },
        "steps": [
            "2¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2.",
            "Doubling ten times: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024."
        ],
        "result": "2 to the power of 10 is 1,024."
    },
    "interpretation": "A negative exponent means a reciprocal (2⁻³ = 1/8), and a fractional exponent means a root (9^0.5 = √9 = 3).",
    "assumptions": [
        "Answers are real numbers only."
    ],
    "limitations": [
        "A negative base with a non-whole exponent, such as (−8)^0.5, has no real answer and is rejected. Cube roots of negatives need the exponent exactly 1/3, which a decimal cannot represent.",
        "Non-integer results are shown to 12 significant digits."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "Why is any number to the power 0 equal to 1?",
            "answer": "Each step down in power divides by the base: 2³ = 8, 2² = 4, 2¹ = 2, so 2⁰ = 2 ÷ 2 = 1. The same holds for every non-zero base."
        },
        {
            "question": "What is 0 to the power 0?",
            "answer": "It is taken as 1 by convention in algebra and combinatorics, which is what this calculator shows; in calculus it is treated as an indeterminate form."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Log Calculator",
            "url": "https://calculators.geekmidst.com/calculators/log-calculator"
        },
        {
            "name": "Number Sequence Calculator",
            "url": "https://calculators.geekmidst.com/calculators/number-sequence-calculator"
        },
        {
            "name": "Compound Interest Calculator",
            "url": "https://calculators.geekmidst.com/calculators/compound-interest-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}