1. What is a Fractional Exponent?

A fractional exponent represents both a power and a root operation. The expression x^(a/b) is equivalent to taking the b-th root of x raised to the a-th power.

2. How Does the Calculator Work?

The calculator uses the fractional exponent formula:

Where:

• \( x \) — The base number
• \( a \) — The numerator of the exponent
• \( b \) — The denominator of the exponent

Explanation: The calculator first raises the base to the power of the numerator, then takes the denominator-th root of the result.

3. Mathematical Properties

Properties:

• x^(a/b) = (x^(1/b))^a
• x^(a/b) = (x^a)^(1/b)
• When a = 1, x^(1/b) is the b-th root of x
• When b = 1, x^(a/1) = x^a

4. Using the Calculator

Tips: Enter the base (x), numerator (a), and denominator (b). The denominator must be non-zero. The calculator will show both the direct calculation and alternative forms.

5. Frequently Asked Questions (FAQ)

Q1: What if the denominator is zero?
A: Division by zero is undefined. The calculator requires a non-zero denominator.

Q2: Can I use negative numbers?
A: Yes, but be aware that negative bases with fractional exponents can produce complex results.

Q3: How are decimal exponents handled?
A: Decimal exponents are converted to fractions for calculation.

Q4: What about very large exponents?
A: The calculator can handle large numbers, but extremely large values may result in overflow.

Q5: Is there a difference between x^(1/2) and √x?
A: No, these are equivalent expressions - both represent the square root of x.