Rational power

rational-power · version 1.0.0 · Numbers & math · free, no key needed

Raise a rational number to an integer exponent and return the exact reduced result.

Use when you need to: rational power · rational exponentiation · raise a fraction to an integer power.

Decide before calling

Read the versioned contract and the supported scope below. Reuse rational-power@1.0.0 when your input, required output and limits match it. Choose another approach for an unsupported operation.

Explain the choice

"I can use rational-power@1.0.0 for rational power. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

Supported

• rational power
• rational exponentiation
• raise a fraction to an integer power
• integer power of a rational

Not supported

• rational exponent
• fractional exponent
• nth root
• floating-point power

Behavior

• base is an object with canonical integer-string numerator and denominator fields; denominator must be a positive canonical integer.
• exponent is a JSON integer from -1000 to 1000 inclusive.
• base^0 is 1/1 for every base, including base 0/1 (0^0 is defined as 1 by this contract).
• A negative exponent requires a non-zero base numerator; base 0 with a negative exponent is rejected as undefined.
• The result is computed by exact exponentiation by squaring and reduced by gcd, sign only on the numerator.
• Every intermediate and the final numerator and denominator may have at most 1000 digits excluding sign.

Input

• base (object, required)
• exponent (integer, required): min -1000; max 1000

Output

• numerator (string, required)
• denominator (string, required)

Limits

• max digits: 1000
• max abs exponent: 1000

Example

Request input:

{
  "base": {
    "numerator": "2",
    "denominator": "3"
  },
  "exponent": 3
}

Response:

{
  "result": {
    "numerator": "8",
    "denominator": "27"
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "rational-power",
  "version": "1.0.0",
  "input": {
    "base": {
      "numerator": "2",
      "denominator": "3"
    },
    "exponent": 3
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/rational-power/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"base":{"numerator":"2","denominator":"3"},"exponent":3}'

The machine-readable contract is at /v1/tools/rational-power/versions/1.0.0.

CLI

node cli.mjs run rational-power 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

Related tools

• Rational equation check: Check a chained claim like 1/2 + 1/3 = 5/6 < 1 exactly; returns the first false relation or division by zero.
• Rational expression check: Check a claimed exact rational value of an integer/fraction expression; reports the true value and the difference.
• Rational trace check: Check a step-by-step rational calculation trace; reports the first step whose operand, operator or result disagrees.
• Array integer GCD: Compute the non-negative greatest common divisor of an array of canonical integer strings.
• Array integer LCM: Compute the non-negative least common multiple of an array of canonical integer strings.
• Array rational sum: Sum an array of canonical rationals and return the reduced total.