Desmos Calculator Fraction Exponent And Radical

Fraction Exponent and Radical Formula:

\[ \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} \] \[ \sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}} \]

Fraction Exponent Result:

Radical Result (n-th root):

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1. What is Fraction Exponent and Radical?

The fraction exponent and radical calculator computes the result of raising a fraction to a power and finding the root of a fraction. These operations are fundamental in algebra and higher mathematics.

2. How Does the Calculator Work?

The calculator uses these mathematical formulas:

\[ \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} \] \[ \sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}} \]

Where:

\( a \) — Numerator (unitless)
\( b \) — Denominator (unitless, must be non-zero)
\( n \) — Exponent (unitless)

Explanation: The calculator first computes the fraction a/b, then raises it to the power n for the exponent result, and computes the n-th root for the radical result.

3. Mathematical Explanation

Details: Fraction exponents follow the power of quotient rule, while radicals can be expressed as exponents with fractional values (e.g., square root is exponent 1/2).

4. Using the Calculator

Tips: Enter numerator, denominator (must be non-zero), and exponent. The calculator will compute both the exponent result and the corresponding radical (root) result.

5. Frequently Asked Questions (FAQ)

Q1: What if my denominator is zero?
A: Division by zero is undefined. The denominator must be a non-zero value.

Q2: Can I use negative exponents?
A: Yes, negative exponents represent reciprocals (e.g., x⁻ⁿ = 1/xⁿ).

Q3: What about complex numbers?
A: This calculator returns real number results. Complex results will show as errors.

Q4: How precise are the results?
A: Results are rounded to 4 decimal places for readability.

Q5: Can I use fractional exponents?
A: Yes, fractional exponents are supported (e.g., 0.5 for square root).