Rational Exponents Calculator
How It Works
This rational exponents calculator uses established formulas to provide accurate results.
The basic rule:
- a^(m/n) = (ⁿ√a)^m = ⁿ√(aᵐ)
- a^(1/n) = ⁿ√a
- a^(m/n) = (a^(1/n))^m
Results are estimates. Consult a professional for critical decisions.
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Explore Allday Everyday Math →Frequently Asked Questions
What is a rational exponent?
A rational exponent is a fraction used as an exponent. For example, 8^(2/3) means take the cube root of 8 and then square it. The denominator is the root and the numerator is the power.
How do I convert a radical to an exponent?
The nth root of a is a^(1/n). So √x = x^(1/2), ∛x = x^(1/3), etc. If there is also a power, like (∛x)², it becomes x^(2/3).
Which do I do first, the root or the power?
Mathematically, it does not matter — (ⁿ√a)^m = ⁿ√(aᵐ). But in practice, taking the root first usually keeps numbers smaller and easier to compute.