Problem
Interpret numerator / denominator as a positive rational number, then raise it to power. This task returns a real number rather than an exact fraction; it covers the real-exponent part of the Rational Numbers reference.
Implement rational_to_real_power(numerator, denominator, power).
Input
numerator: The positive numerator.
denominator: The positive denominator.
power: The real-valued exponent.
Output
Return (numerator / denominator) raised to power.
Constraints
1 ≤ numerator, denominator ≤ 100. −6 ≤ power ≤ 6, with at most two decimal places. Answers are accepted within absolute or relative error 0.000001.
Examples
Input:
power = 0.5
numerator = 9
denominator = 4
Expected output:
expected = 1.5Input:
double power = 0.5;
long long numerator = 9;
long long denominator = 4;
Expected output:
double expected = 1.5;Input:
double power = 0.5;
long numerator = 9;
long denominator = 4;
Expected output:
double expected = 1.5;Explanation
An exponent of 0.5 takes the positive square root: √(9/4) = 3/2 = 1.5.
Input:
power = -1.0
numerator = 2
denominator = 5
Expected output:
expected = 2.5Input:
double power = -1.0;
long long numerator = 2;
long long denominator = 5;
Expected output:
double expected = 2.5;Input:
double power = -1.0;
long numerator = 2;
long denominator = 5;
Expected output:
double expected = 2.5;Explanation
The exponent −1 takes the reciprocal: 5/2 = 2.5.
How to approach it
Try on your own first, then open one hint at a time.
Hint 1
Treat the fraction as one positive real value before applying the exponent.
Hint 2
Use floating-point exponentiation directly, since the answer is approximate.
Hint 3
Be careful with negative and fractional-looking exponents, and keep enough precision for the tolerance.
Expected complexity
O(1) time, O(1) extra space
References
This challenge is adapted for CodeUtility. Follow the statement and constraints above.