1. What Are Powers of Fractions and Decimals?

Powers of fractions and decimals involve raising these numbers to a certain exponent. For example, (1/2)^3 = 1/8 or 0.5^3 = 0.125. This calculator helps compute such values with step-by-step solutions.

2. How Does the Calculator Work?

The calculator performs two types of calculations:

Where:

• \( a \) — Numerator (any real number)
• \( b \) — Denominator (any non-zero real number)
• \( d \) — Decimal value (any real number)
• \( n \) — Exponent (any real number)

3. Mathematical Explanation

Fraction Power: \((a/b)^n = a^n / b^n\)
Decimal Power: Follows the standard exponentiation rules for real numbers.

Special cases:

• Any number to the power of 0 is 1
• Negative exponents represent reciprocals: \( x^{-n} = 1/x^n \)
• Fractional exponents represent roots: \( x^{1/n} = \sqrt[n]{x} \)

4. Using the Calculator

Instructions: Select calculation type (fraction or decimal), enter the required values, and click "Calculate". The calculator will show the result and step-by-step solution.

5. Frequently Asked Questions (FAQ)

Q1: Can I use negative exponents?
A: Yes, negative exponents are supported. They will calculate the reciprocal of the positive power.

Q2: What about fractional exponents?
A: Yes, the calculator supports fractional exponents which represent roots.

Q3: How precise are the calculations?
A: Calculations are performed with PHP's floating-point precision (typically about 14 decimal digits).

Q4: What happens if I enter zero as denominator?
A: The calculator will show an error as division by zero is undefined.

Q5: Can I calculate complex numbers?
A: This calculator only handles real number results. Complex results will show as errors.