# Rational Exponents

Related Topics:
Common Core (The Real Number System)
Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)must equal 5.

Common Core: HSN-RN.A.1

Zero, Negative, and Fractional Exponents.
Zero Exponents - two explanations
Two explanations for why a number raised to the zero power must equal 1.

Negative Exponents
Working with negative exponents. Rational Exponents 1
Part 1 covers the meaning of a fractional exponent when the numerator is 1, and provides examples. Rational Exponents 2
Part 2 covers the meaning of a fractional exponent, and provides examples. Rational Exponents 3
Part 3 shows examples working with radicals and fractional exponents. Rational Exponents 4
Part 4 shows examples working with radicals and fractional exponents. Rational Exponents 5
Part 5 shows more problems examples working with radicals and fractional exponents, and how to write as a single radical. Rational Exponents (Part 1)
An introduction to rational (or fractional) exponents. Rational Exponents (Part 2) Rational Exponents (Part 3)
Convert between rational exponents and radical expressions. Rational Exponents (part 4). Introduction to Fractional Exponents and Radicals.
This video explains how fractional exponents and radicals relate. The video includes multiple examples including some with negative exponents that are fractions and fractions to a negative fractional power.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.