{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"exponent"},"result":{"entity_type":"calculator","id":"exponent","calculator_id":"exponent","canonical_url":"https://tttkmbb.com/math/exponent","name":"Exponent Calculator","title":"Exponent Calculator – Powers with Integer, Negative and Fractional Exponents","category":"math","category_name":"Math","tool_name":"calculate_exponent","featured_mcp_tool":false,"description":"Raises a base to any real exponent (base^exponent), including negative and fractional exponents, and reports the reciprocal and a scientific-notation form.","use_when":"You need a power such as 2^10, 1.05^30 or 8^(1/3), or a quick check of how large a power gets.","do_not_use_when":"You need the exponent that produces a given result (use logarithm) or the n-th root with sign handling for negatives (use nth-root).","inputs":[{"name":"base","label":"Base","type":"number","required":true,"min":-1000000000,"max":1000000000,"description":"The number being multiplied by itself.","example":2},{"name":"exponent","label":"Exponent","type":"number","required":true,"min":-1000,"max":1000,"description":"The power; may be negative or fractional. A negative base requires an integer exponent.","example":10}],"outputs":[{"name":"result","label":"Result","type":"number","decimals":10,"description":"base raised to the exponent."},{"name":"scientific_notation","label":"Scientific notation","type":"string","decimals":4,"description":"The result with 6 significant digits, e.g. '1.024 × 10^3'."},{"name":"reciprocal","label":"Reciprocal","type":"number","decimals":10,"description":"1 / result = base^(−exponent) (omitted when the result is 0)."},{"name":"expression","label":"Expression","type":"string","decimals":4,"description":"The evaluated power as text."}],"input_schema":{"type":"object","properties":{"base":{"description":"The number being multiplied by itself.","type":"number","minimum":-1000000000,"maximum":1000000000,"examples":[2]},"exponent":{"description":"The power; may be negative or fractional. A negative base requires an integer exponent.","type":"number","minimum":-1000,"maximum":1000,"examples":[10]}},"additionalProperties":false,"required":["base","exponent"]},"output_schema":{"type":"object","properties":{"result":{"description":"base raised to the exponent.","type":"number"},"scientific_notation":{"description":"The result with 6 significant digits, e.g. '1.024 × 10^3'.","type":"string"},"reciprocal":{"description":"1 / result = base^(−exponent) (omitted when the result is 0).","type":"number"},"expression":{"description":"The evaluated power as text.","type":"string"}}},"formula":"result = base^exponent; for a fractional exponent p/q: base^(p/q) = (base^(1/q))^p; base^(−n) = 1 / base^n","sources":[{"name":"Wikipedia – Exponentiation","url":"https://en.wikipedia.org/wiki/Exponentiation","type":"reference","retrieved_at":"2026-09-23"},{"name":"Wolfram MathWorld – Power","url":"https://mathworld.wolfram.com/Power.html","type":"reference","retrieved_at":"2026-09-23"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"2^10","inputs":{"base":2,"exponent":10},"expected":{"result":1024,"scientific_notation":"1.024 × 10^3","reciprocal":0.0009765625,"expression":"2^10 = 1024"},"url":"https://tttkmbb.com/api/v1/calculate/exponent?base=2&exponent=10"},{"name":"4^1.5","inputs":{"base":4,"exponent":1.5},"expected":{"result":8,"reciprocal":0.125},"url":"https://tttkmbb.com/api/v1/calculate/exponent?base=4&exponent=1.5"}],"faq":[{"q":"Why is a negative base with a fractional exponent rejected?","a":"(−8)^(1/3) has no unique real value in general (the principal value is complex). Use nth-root, which returns the real root −2 for odd roots."},{"q":"What is 0^0?","a":"The calculator returns 1, the convention used in combinatorics and by most programming languages; some contexts treat it as undefined."}],"tags":["exponent","power","raise to the power","squared","cubed","negative exponent"],"related":[{"calculator_id":"nth-root","reason":"Inverse operation: the root of a number."},{"calculator_id":"logarithm","reason":"Find the exponent from the result."},{"calculator_id":"scientific-notation","reason":"Express very large or small powers compactly."}],"links":{"html":"https://tttkmbb.com/math/exponent","markdown":"https://tttkmbb.com/math/exponent.md","json":"https://tttkmbb.com/math/exponent.json","api":"https://tttkmbb.com/api/v1/calculate/exponent","schema":"https://tttkmbb.com/api/v1/calculators/exponent","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-23"},"timestamp":"2026-09-23T23:23:00Z"}