Fractional Exponent Rule

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A fractional exponent represents a root

The Formula

a^(m/n) = ⁿ√(aᵐ)

Variables & Symbols

a, b

Base numbers

m, n

Exponents

When to Use This Formula

  • Simplifying exponential expressions
  • Solving exponential equations

Worked Examples

Example 1

Problem:

Example: a^(m/n) = ⁿ√(aᵐ)

Solution: Apply the rule

Step-by-Step:

1

Identify the bases and exponents

2

Apply the rule

3

Simplify

Common Mistakes to Avoid

  • Misapplying the rule
  • Sign errors

Real-World Applications

1

Scientific notation

2

Compound interest

3

Population growth

Practice Problems

Problem 1: Apply this rule

Show Answer

Answer: Simplified expression

Related Formulas

logarithm rules

View Formula →

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