1. What is the Dividing Fractions with Exponents Rule?

The rule states that when you have a fraction raised to an exponent, it's equivalent to raising both the numerator and denominator to that exponent separately, then dividing them. This is a fundamental exponent rule in algebra.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( a \) — Numerator of the fraction
• \( b \) — Denominator of the fraction
• \( c \) — Exponent

Explanation: The exponent applies to both the numerator and denominator separately, following the rule of exponents for fractions.

3. Importance of the Rule

Details: This rule is essential for simplifying complex algebraic expressions, solving equations with fractional exponents, and understanding the properties of exponents in mathematics.

4. Using the Calculator

Tips: Enter the numerator (a), denominator (b must be non-zero), and the exponent (c). The calculator will show the step-by-step calculation.

5. Frequently Asked Questions (FAQ)

Q1: Does this rule work with negative exponents?
A: Yes, the rule applies to all real number exponents, including negative ones. A negative exponent would create a reciprocal of the fraction.

Q2: What if the denominator is zero?
A: Division by zero is undefined. The calculator requires a non-zero denominator.

Q3: Can this be applied to more complex fractions?
A: Yes, the rule applies to any fraction, even those with variables or more complex expressions in numerator and denominator.

Q4: How is this different from multiplying exponents?
A: This rule is specifically for exponents applied to fractions, while exponent multiplication rules apply when multiplying like bases.

Q5: Does this work with fractional exponents?
A: Yes, the rule works with any real number exponent, including fractions (roots).