{
  "id": "exponent",
  "version": "0303fbfb362f",
  "status": "published",
  "name": "Exponent Calculator",
  "question": "What is a number to an exponent?",
  "summary": "Raises a base to an exponent, or finds the exponent or the base from the other two numbers.",
  "category": "math",
  "subcategory": "arithmetic",
  "url": "https://www.acalculator.org/math/exponent-calculator",
  "markdown": "https://www.acalculator.org/math/exponent-calculator.md",
  "kind": "formulas",
  "method": "r = bⁿ: the result r is the base b raised to the exponent n.",
  "assumptions": [
    "Real numbers only: a negative base needs a whole-number exponent.",
    "0⁰ and 0 raised to a negative power are undefined, so they have no answer.",
    "Solving for the base with an even whole exponent gives two answers, a positive and a negative one."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "base": {
        "title": "Base",
        "description": "The number that is multiplied by itself.",
        "type": "number"
      },
      "exponent": {
        "title": "Exponent",
        "description": "The power: how many times the base is used as a factor.",
        "type": "number"
      },
      "answer": {
        "title": "Result",
        "description": "The base raised to the exponent.",
        "type": "number"
      }
    }
  },
  "solve": {
    "fillAny": 2,
    "variables": [
      "base",
      "exponent",
      "answer"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "base": {
      "label": "Base",
      "description": "The number that is multiplied by itself.",
      "format": "number"
    },
    "exponent": {
      "label": "Exponent",
      "description": "The power: how many times the base is used as a factor.",
      "format": "number"
    },
    "result": {
      "label": "Result",
      "description": "The base raised to the exponent.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "base": 2,
      "exponent": 3
    },
    "outputs": {
      "result": 8
    },
    "text": "2 to the power of 3 is 8."
  },
  "examples": [
    {
      "given": {
        "base": 2,
        "exponent": 3
      },
      "expect": {
        "answer": 8
      },
      "source": "hand calculation in content.mdx: 2 × 2 × 2 = 8; OpenStax, Elementary Algebra 2e, §6.2 Use Multiplication Properties of Exponents. https://openstax.org/books/elementary-algebra-2e/pages/6-2-use-multiplication-properties-of-exponents"
    },
    {
      "given": {
        "base": 10,
        "exponent": -2
      },
      "expect": {
        "answer": 0.01
      },
      "source": "hand calculation in content.mdx: 10⁻² = 1 ÷ 10² = 0.01; OpenStax, Elementary Algebra 2e, §6.2 Use Multiplication Properties of Exponents. https://openstax.org/books/elementary-algebra-2e/pages/6-2-use-multiplication-properties-of-exponents"
    },
    {
      "given": {
        "base": -2,
        "exponent": 3
      },
      "expect": {
        "answer": -8
      },
      "source": "hand calculation in content.mdx: (−2) × (−2) × (−2) = −8; OpenStax, Elementary Algebra 2e, §6.2 Use Multiplication Properties of Exponents. https://openstax.org/books/elementary-algebra-2e/pages/6-2-use-multiplication-properties-of-exponents"
    },
    {
      "given": {
        "base": 2,
        "answer": 1024
      },
      "expect": {
        "exponent": 10
      },
      "source": "hand calculation in content.mdx: 2¹⁰ = 1,024, so n = log₂ 1,024 = 10; OpenStax, Elementary Algebra 2e, §6.2 Use Multiplication Properties of Exponents. https://openstax.org/books/elementary-algebra-2e/pages/6-2-use-multiplication-properties-of-exponents"
    },
    {
      "given": {
        "exponent": 2,
        "answer": 81
      },
      "expect": {
        "base": 9
      },
      "source": "hand calculation in content.mdx: 9² = 81 and (−9)² = 81; OpenStax, Elementary Algebra 2e, §6.2 Use Multiplication Properties of Exponents. https://openstax.org/books/elementary-algebra-2e/pages/6-2-use-multiplication-properties-of-exponents"
    },
    {
      "given": {
        "base": 2.5,
        "exponent": 2.5
      },
      "expect": {
        "answer": 9.882117688026186
      },
      "source": "hand calculation in content.mdx: 2.5^2.5 = e^(2.5 × ln 2.5); Python 3: 2.5 ** 2.5 = 9.882117688026186; OpenStax, Elementary Algebra 2e, §6.2 Use Multiplication Properties of Exponents. https://openstax.org/books/elementary-algebra-2e/pages/6-2-use-multiplication-properties-of-exponents"
    }
  ],
  "sources": [
    "OpenStax, Elementary Algebra 2e, §6.2 Use Multiplication Properties of Exponents. https://openstax.org/books/elementary-algebra-2e/pages/6-2-use-multiplication-properties-of-exponents"
  ],
  "related": [],
  "changelog": [
    {
      "date": "2026-09-28",
      "note": "0⁰, 0 to a negative power, and values past double range say why there is no answer."
    },
    {
      "date": "2026-09-29",
      "note": "Worked examples name a published reference for their rule."
    }
  ]
}